What are the different ways a derivative can be interpreted as? -There are many different ways a derivative can be interpreted. Usually a problem does not even say find the derivative, it is going to give you other words and you are just going to have to know it means take the derivative. In everything we learned so far in calculus it dealt with derivatives, so from 1-3 there were plenty of key words used, and different ways a derivative could have been interpreted.
Here are some of the different ways: f'(x) dy/dx y' d/dx [f(x)] Dx[y] Slope of a tangent line Speed Velocity Acceleration Rate of Change First derivative test
What have we used derivatives for? 1. The limit process 2. The slope of a tangent line 3. An instantaneous rate of change 4. Finding Critical numbers, absolute max’s/min’s, relative max/min’s 5. Finding the rate of change 6. Regular Derivatives
*What are the different ways a derivative can be interpreted as? 1. First it can be in several different function forms such as: f'(x), dy/dx, d/dx, y', [f(x)], etc. 2. Next, it can be expressed in various phrases, which don't come right out and say "Take the derivative"; it's pretty much just implied or understood..phrases such as: -"slope m of the tangent line" or "slope of the graph of the function"=take derivative -"find the derivative using the limit process" (although this says "derivative" in it, it tells you to take it the long way.., i.e. f(x+*x)-f(x)/(*x)..where * is delta x. However, you can always use the shorter method, too. -"equation of a line that is tangent to the graph of f.." = take the derivative of f, and you'll have to find the slope of the line -"alternative form of the derivative" or "use the rules of differentiation.."=the shorter method to take the derivative -"determine all values of x at which the graph has a horizontal tangent"=take derivative and set it equal to zero -"determine the velocity function for..."=take the derivative and leave it in the form of #'s and variables...i.e-3x^2 -"instantaneous velocity=velocity=TAKE DERIVATIVE -"find the acceleration of..."=2nd derivative -"use the product/quotient/chain rule.."=take the derivative using those methods -"find the RATE OF CHANGE.."=take derivative of the function(s) given -"determine AVERAGE VELOCITY...over the interval [a,b]=take the numbers in the interval, which are your x-values, and plug them into the original equation you are given. Then once you have your two points, find the slope -implicit differentiation=take derivative the same way, but with respect to y or any other specific variable present -maxs/mins,critical values, "increasing/decreasing"=take derivative and set it equal to zero. Set up intervals using the x-values you found and then plug in numbers on each interval. -Dealing with pictures of GRAPHS: --the derivative of diagonal lines are horizontal lines (if the diagonal line is going down, then the horizontal line will be negative..and vice versa..) --derivative of a horizontal line is a horizontal line at 0 --derivative of a parabola is a diagonal line (if the parabola is facing up, then the diagonal line will also be going up, and vice versa..) **I think I pretty much answered both questions in all of that^^^well, I hope I did..
What are the different ways a derivative can be interpreted as? In other words I think I am looking for key words to recognize that a derivative is necessary dy/dx
y ’
f ’(x)
d/dx
d/dx [f(x)]
Dx [y]
limit process Short cut method for a derivative slope of a graph at a single point slope of a tangent line slope of a curve at a point rate of change Speed instantaneous Velocity average velocity Acceleration Use product rule Use quotient rule Chain rule General power rule Implicit differentiation With respect to Related rates Critical numbers Extreme values Max Min Relative Extrema Absolute extrema Rolles thorem Mean value thorem Find all values of c on an interval where f’(c)=0 First derivative test Increasing Decreasing Change of direction
So far what have you used the derivative for? Finding dy/dx
finding y ’
Finding f ’(x)
Finding d/dx
Finding d/dx [f(x)]
Finding Dx [y]
Using the limit process Using Short cut method for a derivative Finding the slope of a graph at a single point Finding the slope of a tangent line Finding the slope of a curve at a point Finding all values of x where there is a horizontal tangent/ if there are any x values where there is a horizontal tangent or not Solving for a rate of change Finding the Speed Finding the instantaneous Velocity Finding the average velocity Finding the Acceleration Using the product rule Using the quotient rule Using the Chain rule Using the General power rule Practicing Implicit differentiation Solving With respect to Finding Related rates Finding Critical numbers Finding Extreme values Deciphering if there is/ Finding the Max Deciphering if there is/ Finding the Min Finding the Relative Extrema Finding the Absolute extrema Using Rolles thorem Using the Mean value thorem Finding all values of c on an interval where f’(c)=0 Using the First derivative test Find where a graph is Increasing or Decreasing When dealing with a Change of direction Also When asked questions about a graph involving any of the problems listed above
What are the different ways a derivative can be interpreted as?
There are many different ways in which a derivative can be interpreted. There are many different notations, meanings, and other things to denote them.
Some of the ways:
d/dx dy/x d/dy y' f'(x) g'(x) d/dx[f(x)] Dx[y] slope of a tangent line slope of a curve at a point rate of change velocity speed acceleration instantaneous velocity "with respect to"
What do we use derivatives for?
We use them for:
taking a derivative finding a derivative the limit process finding rates of change finding implicit derivatives finding the equation of a tangent line finding the slope of a tangent line finding the equation of a secant line using the chain rule using the product rule using the quotient rule position, velocity, and accleration (PVA) functions finding extrema on a closed interval finding critical numbers absolute max absolute min relative max relative min using Rolle's Theorem using the Mean Value Theorem
A derivative can be interpreted as: d/dx dx/dy Dx y’ f’(x) slope of a tangent line slope of a horizontal tangent line equation of a tangent line rate of change velocity average velocity instantaneous velocity acceleration
Derivatives are used for: general power rule implicit derivative limit process product rule quotient rule chain rule related rates max min critical numbers extreme values relative extrema absolute extrema Rolle ’s Theorem Mean Value Theorem First Derivative Test change of direction
What are the different ways a derivative can be interpreted as? -There are many different ways instructions can tell you to take a derivative. Usually, directions do not come out and say ‘find the derivative’. They might say something like ‘find the slope of a tangent line’ or ‘find the average velocity’.
The easy ways one can recognize a derivative: -dy/dx -y` -f `(x) -d/dx -Dx[y]
Key words/phrases that indicate a derivative is involved: -find the slope m of a tangent line -find the equation of a line that is tangent to f(x) -speed -velocity -acceleration -rate of change -first derivative test -limit process -slope of a graph at a single point -quotient/product rule -extreme values -critical numbers -Rolle’s Theorem -Mean Value Theorem -find all values of c on an interval where f `(c)=0
So far, what have you used the derivative for?
So far this year, we have used derivatives to find f `(x) >basic derivative -finding the slope of a graph at a point -solving for rate of change -using the general power rule, -using the limit process, -using the product rule, -using the quotient rule, -using the chain rule, -finding critical numbers, -finding extreme values, -finding implicit derivatives, -finding the max and min, -using the mean value theorem, -using Rolle’s theorem, -using first derivative test, -solving for speed -finding instantaneous velocity -finding average velocity (slope) -finding relative and absolute extrema -dealing with change in direction (inclining and declining)
what are the different ways a derivative can be interpreted as?
dy/x d/dx d/dx[f(x)] Dx[y] d/dy f'(x) g'(x) y' slope of a tangent line slope of a curve at a point speed velocity instantaneous velocity acceleration rate of change
we have used derivatives for:
implicit derivatives general power rules the limit process quotient, product, and chain rules related rates max and mins critical numbers relative extrema extreme values absolute extrema Rolle's Theorem mean value theorem change of direction first derivative test
f'(x) y' dy/dx dx/dt d/dx dy/x slope of tangent line slope of a curve instantaneous velocity rate of change acceleration velocity speed
we used derivatives in chapters 2-3 so far, in problems such as:
Limit Process General Power rule Chain Rule Quotient Rule Product Rule Related Rate Finding Critical numbers (max & min) Rolle's Theorem MVT (Mean Value Theorem) The First Derivative Test
What are the different ways a derivative can be interpreted as? So far what have you used the derivative for?
So, this question is basically asking what derivatives are used for so far from what we've learned. Derivatives can be used for everything from finding the slope of a tangent line to determining when the universe will end. Some examples of things we have used them for are: slope velocity acceleration speed position dividing by 0 extrema relative extrema absolute extrema critical numbers
There are also a lot of ways they can say to derivative in instructions such as: Find the slope of the tan find dy/dx find f'(x) find y' find the instantaneous velocity find dx/dt find d/dx find the rate of change find the critical numbers find the extrema
There are many things derivatives can be used for and these are most of the ones that we learned so far.
Derivatives can be interpreted in many different ways. Since derivatives are used to find pretty much everything in calculus, then they have to be interchangable.
Derivatives can be interpreted by the following words, symbols, letters, and/or phases.
-f'(x) -dy/dx -y' -d/dx [f(x)] -Dx[y] -Slope of a tangent line -Speed -Velocity -Acceleration -Rate of Change -First derivative test -Second derivative -third derivative -etc
Derivatives are used for alot in calculus. there are many different ways derivatives are used: - limit process - slope of a tangent line - instantaneous rate of change - Critical numbers - absolute maximums and minimums - relative maximums and minimums - rate of change - Derivatives
what are the different ways derivatives can be interpreted as? uhmm.....y', f', dy/dx, dx/dy, dy/dt, dx/dt, and other variations of those
so far, we've used derivatives for stuff like the limit process, slope of a tangent line, instantaneous rate of change, critical numbers, absolute maximums and minimums, relative maximums and minimums, rates of change, and so much more
What are the different ways a derivative can be interpreted as?
ReplyDelete-There are many different ways a derivative can be interpreted. Usually a problem does not even say find the derivative, it is going to give you other words and you are just going to have to know it means take the derivative. In everything we learned so far in calculus it dealt with derivatives, so from 1-3 there were plenty of key words used, and different ways a derivative could have been interpreted.
Here are some of the different ways:
f'(x)
dy/dx
y'
d/dx [f(x)]
Dx[y]
Slope of a tangent line
Speed
Velocity
Acceleration
Rate of Change
First derivative test
What have we used derivatives for?
1. The limit process
2. The slope of a tangent line
3. An instantaneous rate of change
4. Finding Critical numbers, absolute max’s/min’s, relative max/min’s
5. Finding the rate of change
6. Regular Derivatives
*What are the different ways a derivative can be interpreted as?
ReplyDelete1. First it can be in several different function forms such as:
f'(x), dy/dx, d/dx, y', [f(x)], etc.
2. Next, it can be expressed in various phrases, which don't come right out and say "Take the derivative"; it's pretty much just implied or understood..phrases such as:
-"slope m of the tangent line" or "slope of the graph of the function"=take derivative
-"find the derivative using the limit process" (although this says "derivative" in it, it tells you to take it the long way.., i.e. f(x+*x)-f(x)/(*x)..where * is delta x. However, you can always use the shorter method, too.
-"equation of a line that is tangent to the graph of f.." = take the derivative of f, and you'll have to find the slope of the line
-"alternative form of the derivative" or "use the rules of differentiation.."=the shorter method to take the derivative
-"determine all values of x at which the graph has a horizontal tangent"=take derivative and set it equal to zero
-"determine the velocity function for..."=take the derivative and leave it in the form of #'s and variables...i.e-3x^2
-"instantaneous velocity=velocity=TAKE DERIVATIVE
-"find the acceleration of..."=2nd derivative
-"use the product/quotient/chain rule.."=take the derivative using those methods
-"find the RATE OF CHANGE.."=take derivative of the function(s) given
-"determine AVERAGE VELOCITY...over the interval [a,b]=take the numbers in the interval, which are your x-values, and plug them into the original equation you are given. Then once you have your two points, find the slope
-implicit differentiation=take derivative the same way, but with respect to y or any other specific variable present
-maxs/mins,critical values, "increasing/decreasing"=take derivative and set it equal to zero. Set up intervals using the x-values you found and then plug in numbers on each interval.
-Dealing with pictures of GRAPHS:
--the derivative of diagonal lines are horizontal lines (if the diagonal line is going down, then the horizontal line will be negative..and vice versa..)
--derivative of a horizontal line is a horizontal line at 0
--derivative of a parabola is a diagonal line (if the parabola is facing up, then the diagonal line will also be going up, and vice versa..)
**I think I pretty much answered both questions in all of that^^^well, I hope I did..
What are the different ways a derivative can be interpreted as?
ReplyDeleteIn other words I think I am looking for key words to recognize that a derivative is necessary
dy/dx
y ’
f ’(x)
d/dx
d/dx [f(x)]
Dx [y]
limit process
Short cut method for a derivative
slope of a graph at a single point
slope of a tangent line
slope of a curve at a point
rate of change
Speed
instantaneous Velocity
average velocity
Acceleration
Use product rule
Use quotient rule
Chain rule
General power rule
Implicit differentiation
With respect to
Related rates
Critical numbers
Extreme values
Max
Min
Relative Extrema
Absolute extrema
Rolles thorem
Mean value thorem
Find all values of c on an interval where f’(c)=0
First derivative test
Increasing
Decreasing
Change of direction
So far what have you used the derivative for?
Finding dy/dx
finding y ’
Finding f ’(x)
Finding d/dx
Finding d/dx [f(x)]
Finding Dx [y]
Using the limit process
Using Short cut method for a derivative
Finding the slope of a graph at a single point
Finding the slope of a tangent line
Finding the slope of a curve at a point
Finding all values of x where there is a horizontal tangent/ if there are any x values where there is a horizontal tangent or not
Solving for a rate of change
Finding the Speed
Finding the instantaneous Velocity
Finding the average velocity
Finding the Acceleration
Using the product rule
Using the quotient rule
Using the Chain rule
Using the General power rule
Practicing Implicit differentiation
Solving With respect to
Finding Related rates
Finding Critical numbers
Finding Extreme values
Deciphering if there is/ Finding the Max
Deciphering if there is/ Finding the Min
Finding the Relative Extrema
Finding the Absolute extrema
Using Rolles thorem
Using the Mean value thorem
Finding all values of c on an interval where f’(c)=0
Using the First derivative test
Find where a graph is Increasing or Decreasing
When dealing with a Change of direction
Also When asked questions about a graph involving any of the problems listed above
What are the different ways a derivative can be interpreted as?
ReplyDeleteThere are many different ways in which a derivative can be interpreted. There are many different notations, meanings, and other things to denote them.
Some of the ways:
d/dx
dy/x
d/dy
y'
f'(x)
g'(x)
d/dx[f(x)]
Dx[y]
slope of a tangent line
slope of a curve at a point
rate of change
velocity
speed
acceleration
instantaneous velocity
"with respect to"
What do we use derivatives for?
We use them for:
taking a derivative
finding a derivative
the limit process
finding rates of change
finding implicit derivatives
finding the equation of a tangent line
finding the slope of a tangent line
finding the equation of a secant line
using the chain rule
using the product rule
using the quotient rule
position, velocity, and accleration (PVA) functions
finding extrema on a closed interval
finding critical numbers
absolute max
absolute min
relative max
relative min
using Rolle's Theorem
using the Mean Value Theorem
A derivative can be interpreted as:
ReplyDeleted/dx
dx/dy
Dx
y’
f’(x)
slope of a tangent line
slope of a horizontal tangent line
equation of a tangent line
rate of change
velocity
average velocity
instantaneous velocity
acceleration
Derivatives are used for:
general power rule
implicit derivative
limit process
product rule
quotient rule
chain rule
related rates
max
min
critical numbers
extreme values
relative extrema
absolute extrema
Rolle ’s Theorem
Mean Value Theorem
First Derivative Test
change of direction
What are the different ways a derivative can be interpreted as?
ReplyDelete-There are many different ways instructions can tell you to take a derivative. Usually, directions do not come out and say ‘find the derivative’. They might say something like ‘find the slope of a tangent line’ or ‘find the average velocity’.
The easy ways one can recognize a derivative:
-dy/dx
-y`
-f `(x)
-d/dx
-Dx[y]
Key words/phrases that indicate a derivative is involved:
-find the slope m of a tangent line
-find the equation of a line that is tangent to f(x)
-speed
-velocity
-acceleration
-rate of change
-first derivative test
-limit process
-slope of a graph at a single point
-quotient/product rule
-extreme values
-critical numbers
-Rolle’s Theorem
-Mean Value Theorem
-find all values of c on an interval where f `(c)=0
So far, what have you used the derivative for?
So far this year, we have used derivatives to find f `(x) >basic derivative
-finding the slope of a graph at a point
-solving for rate of change
-using the general power rule,
-using the limit process,
-using the product rule,
-using the quotient rule,
-using the chain rule,
-finding critical numbers,
-finding extreme values,
-finding implicit derivatives,
-finding the max and min,
-using the mean value theorem,
-using Rolle’s theorem,
-using first derivative test,
-solving for speed
-finding instantaneous velocity
-finding average velocity (slope)
-finding relative and absolute extrema
-dealing with change in direction (inclining and declining)
what are the different ways a derivative can be interpreted as?
ReplyDeletedy/x
d/dx
d/dx[f(x)]
Dx[y]
d/dy
f'(x)
g'(x)
y'
slope of a tangent line
slope of a curve at a point
speed
velocity
instantaneous velocity
acceleration
rate of change
we have used derivatives for:
implicit derivatives
general power rules
the limit process
quotient, product, and chain rules
related rates
max and mins
critical numbers
relative extrema
extreme values
absolute extrema
Rolle's Theorem
mean value theorem
change of direction
first derivative test
f'(x)
ReplyDeletey'
dy/dx
dx/dt
d/dx
dy/x
slope of tangent line
slope of a curve
instantaneous velocity
rate of change
acceleration
velocity
speed
we used derivatives in chapters 2-3 so far, in problems such as:
Limit Process
General Power rule
Chain Rule
Quotient Rule
Product Rule
Related Rate
Finding Critical numbers (max & min)
Rolle's Theorem
MVT (Mean Value Theorem)
The First Derivative Test
What are the different ways a derivative can be interpreted as? So far what have you used the derivative for?
ReplyDeleteSo, this question is basically asking what derivatives are used for so far from what we've learned. Derivatives can be used for everything from finding the slope of a tangent line to determining when the universe will end. Some examples of things we have used them for are:
slope
velocity
acceleration
speed
position
dividing by 0
extrema
relative extrema
absolute extrema
critical numbers
There are also a lot of ways they can say to derivative in instructions such as:
Find the slope of the tan
find dy/dx
find f'(x)
find y'
find the instantaneous velocity
find dx/dt
find d/dx
find the rate of change
find the critical numbers
find the extrema
There are many things derivatives can be used for and these are most of the ones that we learned so far.
Derivatives can be interpreted in many different ways. Since derivatives are used to find pretty much everything in calculus, then they have to be interchangable.
ReplyDeleteDerivatives can be interpreted by the following words, symbols, letters, and/or phases.
-f'(x)
-dy/dx
-y'
-d/dx [f(x)]
-Dx[y]
-Slope of a tangent line
-Speed
-Velocity
-Acceleration
-Rate of Change
-First derivative test
-Second derivative
-third derivative
-etc
Derivatives are used for alot in calculus. there are many different ways derivatives are used:
- limit process
- slope of a tangent line
- instantaneous rate of change
- Critical numbers
- absolute maximums and minimums
- relative maximums and minimums
- rate of change
- Derivatives
what are the different ways derivatives can be interpreted as?
ReplyDeleteuhmm.....y', f', dy/dx, dx/dy, dy/dt, dx/dt, and other variations of those
so far, we've used derivatives for stuff like the limit process, slope of a tangent line, instantaneous rate of change, critical numbers, absolute maximums and minimums, relative maximums and minimums, rates of change, and so much more