The different keywords that indicate taking a derivative are: * d/dx = derivative * dx/dy = derivative * Dx = derivative * y’ = derivative of y * f’(x) = derivative of f(x) * slope of a tangent line = derivative * slope of a horizontal tangent line = take the derivative then set equal to 0 * equation of a tangent line = take the derivative then plug it and the given point into a point-slope equation * rate of change = derivative * velocity = derivative * instantaneous velocity = derivative * acceleration = take the derivative twice
Examples of directions: * “Take the derivative of…” * “Find the slope of a tangent line when…” * “Find the slope of a horizontal tangent line when…” * “Find the slope of a curve at…” * “Find the equation of a tangent line when…” * “What is the velocity when…” * “Find the instantaneous velocity when…” * “Find the acceleration when…” * “Find the rate of change when…”
To begin, I will explain what the definition of a derivative is, before giving the example ways to write it. A derivative is a slope of a tangent line, slope of a curve at a point, or the rate of change. There are several ways to represent a derivative, and each way could be used when doing certain problems. Derivatives are also used in rules along with representing things. Derivatives are also used in the quotient rule, product rule, chain rule, power rule, and trig functions. ----------------------------------- Key words: (When you see these words you know to find a derivative) Velocity Tangent slope line Rate of change Speed Acceleration **Out of the three at the top you will usually see two of them in application problems. (Velocity and Rate of change)
The derivative of trig functions: Tan x= sec^2x Csc x= -cscxcotx Cot x= csc^2 Sec x= secxtanx
Examples and Expressions: -All of them mean find the derivative Dy/dx, y’, y”, y”’, ect., f’(x), g’(x), d/dx, [f(x)], Dx[y]
The functions indicating a derivative include: dy/dx; y'; f'(x); [f(x)]; Dx[y]; d/dx ^All these things are telling you to take the derivative. It's just showing it in a simpler form. So for example if the directions said---Find f'(c) when c=1. This means to find the derivative of the equation given to you and then plug in 1 after. Some words indicating a derivative include: *slope of the tangent line *rate of change (acceleration-2 d/dx's, velocity) *equation of the tangent line-take derivative , then use point and slope in point-slope formula y2-y1=m(x2-x1) to get equation *slope of a horizontal tangent line-take derivative, set it equal to zero and solve for x. *find the slope of the graph of the function at the given point-means to take the derivative of the function then plug the x-value of the point into the derivative *f'(x)-1st derivative *f''(x)-2nd derivative *f'''(x)-3rd derivative *find the derivative by the limit process-take the derivative THE LONG WAY. (with the delta x's) *find f'(x) using the deffinition of a derivative-also means to take the derivative the LONG WAY.
What are the different keywords that indicate taking a derivative?
There are many different keywords that indicate or notate taking a derivative of a function, all including:
dy/dx, y'(prime), f'(x) (f prime of x), d/dx[f(x)], Dx[y]
Give examples of direction sets that tell you they want a derivative.
When a textbook or the AP asks you to find a derivative, there are many ways that "taking it" or finding it can be asked to you. You just have to be familiar with the different ways in order to find a derivative in every possible situation.
-Find the derivative (of course, lol) -slope of a tangent line -slope of a curve (at a point) -find the rate of change -find the slope of the graph (find derivative, then plug in x) -instantaneous velocity
Once again, taking the derivative of a function has many ways to do it. You just have to be familiar with the way books word it, in order to find or "take" the derivative correctly.
there are numerous keywords used when taking a derivative:
f'(x) dy/dx y' d/dx [f(x)] Dx[y]
there are also various meanings of derivatives; they could mean:
find slope of a tangent line find slope of a curve find rate of change find the slope of the graph find instantaneous velocity find acceleration and of course, just find the derivative ._.;
although there are many phrases used to ask "find the derivative..." they all point towards the same idea, and some are slightly more specific than others. recognizing the notation is key to what the question is asking of you
There are several ways the book will ask you that means "take the derivative" i guess its to slip you up or just to be jerks haha
Examples:
if f(x)=# f'(x)=? take the derivative y' dy/dx find the slope of the tangent line find the slope of the curve rate of change instantaneos velocity Dx(y)
basically, if you see an apostrophe or dx anywhere before the equation, you should know that you need to take a derivative
dy/dx, y ’, f ’(x), d/dx, d/dx [f(x)], and Dx [y] are all notations used to show that a problem is asking you to find a derivative.
different terms used to ask for derivatives are slope of a tangent line, acceleration, speed, velocity, rate of change, and occasionally gravity on the moon.
What are the different keywords that indicate taking a derivative?
ReplyDeleteThere are key expressions that indicate taking a derivative which are :
dy/dx
y ’
f ’(x)
d/dx
d/dx [f(x)]
Dx [y]
There are also key phrases that indicate taking a derivative which are:
Slope of a tangent line
Speed
Velocity
Acceleration
Rate of Change (( something per something))
Give examples of direction sets that tell you they want a derivative.
Ex: 1 “Find the slope of a tangent line when…”
Ex:2 “Find the slope of a curve at a given point…”
Ex:3 “Find the speed”
Ex:4 “Find the acceleration”
Ex: 5 “Find the velocity”
Ex: 6 ((when asked for any rate of change)) [i.e. cars per minute, gallons per hour, tickets sold per hour etc..]
Ex: 7 When specifically asked to “find dy/dx”
Ex: 8 When specifically asked to “find y ’ ”
Ex: 9 When specifically asked to “find f ’(x)”
Ex: 10 When specifically asked to “find d/dx”
Ex: 11 When specifically asked to “find d/dx [f
(x)]”
Ex: 12 When specifically asked to “find
Dx [y]”
Ex: 13 “Find the derivative of”
The different keywords that indicate taking a derivative are:
ReplyDelete* d/dx = derivative
* dx/dy = derivative
* Dx = derivative
* y’ = derivative of y
* f’(x) = derivative of f(x)
* slope of a tangent line = derivative
* slope of a horizontal tangent line = take the derivative then set equal to 0
* equation of a tangent line = take the derivative then plug it and the given point into a point-slope equation
* rate of change = derivative
* velocity = derivative
* instantaneous velocity = derivative
* acceleration = take the derivative twice
Examples of directions:
* “Take the derivative of…”
* “Find the slope of a tangent line when…”
* “Find the slope of a horizontal tangent line when…”
* “Find the slope of a curve at…”
* “Find the equation of a tangent line when…”
* “What is the velocity when…”
* “Find the instantaneous velocity when…”
* “Find the acceleration when…”
* “Find the rate of change when…”
To begin, I will explain what the definition of a derivative is, before giving the example ways to write it. A derivative is a slope of a tangent line, slope of a curve at a point, or the rate of change. There are several ways to represent a derivative, and each way could be used when doing certain problems. Derivatives are also used in rules along with representing things. Derivatives are also used in the quotient rule, product rule, chain rule, power rule, and trig functions.
ReplyDelete-----------------------------------
Key words: (When you see these words you know to find a derivative)
Velocity
Tangent slope line
Rate of change
Speed
Acceleration
**Out of the three at the top you will usually see two of them in application problems.
(Velocity and Rate of change)
The derivative of trig functions:
Tan x= sec^2x
Csc x= -cscxcotx
Cot x= csc^2
Sec x= secxtanx
Examples and Expressions:
-All of them mean find the derivative
Dy/dx, y’, y”, y”’, ect., f’(x), g’(x), d/dx, [f(x)], Dx[y]
The functions indicating a derivative include:
ReplyDeletedy/dx; y'; f'(x); [f(x)]; Dx[y]; d/dx
^All these things are telling you to take the derivative. It's just showing it in a simpler form.
So for example if the directions said---Find f'(c) when c=1. This means to find the derivative of the equation given to you and then plug in 1 after.
Some words indicating a derivative include:
*slope of the tangent line
*rate of change (acceleration-2 d/dx's, velocity)
*equation of the tangent line-take derivative , then use point and slope in point-slope formula y2-y1=m(x2-x1) to get equation
*slope of a horizontal tangent line-take derivative, set it equal to zero and solve for x.
*find the slope of the graph of the function at the given point-means to take the derivative of the function then plug the x-value of the point into the derivative
*f'(x)-1st derivative
*f''(x)-2nd derivative
*f'''(x)-3rd derivative
*find the derivative by the limit process-take the derivative THE LONG WAY. (with the delta x's)
*find f'(x) using the deffinition of a derivative-also means to take the derivative the LONG WAY.
What are the different keywords that indicate taking a derivative?
ReplyDeleteThere are many different keywords that indicate or notate taking a derivative of a function, all including:
dy/dx, y'(prime), f'(x) (f prime of x), d/dx[f(x)], Dx[y]
Give examples of direction sets that tell you they want a derivative.
When a textbook or the AP asks you to find a derivative, there are many ways that "taking it" or finding it can be asked to you. You just have to be familiar with the different ways in order to find a derivative in every possible situation.
-Find the derivative (of course, lol)
-slope of a tangent line
-slope of a curve (at a point)
-find the rate of change
-find the slope of the graph (find derivative, then plug in x)
-instantaneous velocity
Once again, taking the derivative of a function has many ways to do it. You just have to be familiar with the way books word it, in order to find or "take" the derivative correctly.
there are numerous keywords used when taking a derivative:
ReplyDeletef'(x)
dy/dx
y'
d/dx [f(x)]
Dx[y]
there are also various meanings of derivatives; they could mean:
find slope of a tangent line
find slope of a curve
find rate of change
find the slope of the graph
find instantaneous velocity
find acceleration
and of course, just find the derivative ._.;
although there are many phrases used to ask "find the derivative..." they all point towards the same idea, and some are slightly more specific than others. recognizing the notation is key to what the question is asking of you
There are several ways the book will ask you that means "take the derivative" i guess its to slip you up or just to be jerks haha
ReplyDeleteExamples:
if f(x)=# f'(x)=? take the derivative
y'
dy/dx
find the slope of the tangent line
find the slope of the curve
rate of change
instantaneos velocity
Dx(y)
basically, if you see an apostrophe or dx anywhere before the equation, you should know that you need to take a derivative
What are the different keywords that indicate taking a derivative?
ReplyDeleteThe key expressions that indicate taking a derivative are:
dy/dx
y ’
f’(x)
d/dx
d/dx [f(x)]
Dx [y]
The key phrases that indicate taking a derivative:
Slope of a tangent line
Speed
Velocity
Acceleration
Rate of Change (( something per something))
Give examples of direction sets that tell you they want a derivative:
1. -Find the slope of a tangent line when…
2. -Find the slope of a curve at a given point…
3. -Find the speed
4. -Find the acceleration
5. -Find the velocity
6. -when asked for any rate of change
i.e. cars per minute or gallons per hour
7. -When specifically asked to find dy/dx
8. When specifically asked to find y ’(x)
9. When specifically asked to find f ’(x)
10. When specifically asked to find d/dx
11. When specifically asked to find d/dx [f
(x)]
12. When specifically asked to find
Dx [y]
13. Find the derivative of...
dy/dx, y ’, f ’(x), d/dx, d/dx [f(x)], and Dx [y] are all notations used to show that a problem is asking you to find a derivative.
ReplyDeletedifferent terms used to ask for derivatives are slope of a tangent line, acceleration, speed, velocity, rate of change, and occasionally gravity on the moon.
Some different notations are:
ReplyDeletedy/dx
y'
f'(x)
dx(y)
d/dx[f(x)]
slope of a tangent line
velocity
speed
acceleration
rate of change
Directions could be:
Find the f'
Find the dy/dx
etc.
What is the slope of the tangent line through the point (x,y) for equation n+1?
Find the slope of the curve at (x,y).
Find the speed.
Find the velocity.
Find the acceleration.
Find the rate of change.
And many, many more wordings.
The keywords and forms of equations for finding a derivative are:
ReplyDeletedy/dx
y’
f’(x)
d/dx
d/dx (f(x)
Dx (y)
Slope
Speed
Velocity
Acceleration
Any kind of ratio
Ex. y'x
Ex. Dx(2x)
Ex. Find the speed of ....
Ex. Find the slope of the tangent line at ....
Ex. Find the amount of ....... per ......
what is this.....I don't even.....
ReplyDeletewell, I think I might say that there's a bunch of ways to signal derivatives:
dy/dx
d/dx
y'
f'(x)
d/d(x) f(x)
Dx (y)
now, there's a number of terms and whatnot that help you figure out that you need to find a derivative:
Slope
Speed
Velocity
Acceleration
Tangent line
Secant line
Herp-Derp
DERIVE
DERIVATIVE
FIND THE DERIVATIVE
slope of a Tangent Line
rate of change
and numerous other terms
now, here's a few examples of situations where you have to find the derivatives:
y'x
Dx(4x)
Find the speed
Find the slope of tangent line ***** at (x,y).
Find the rate of change
Find the speed
Find the acceleration
Find the slope of the Secant line
and a whole bunch of other examples
sadly, derivatives shall be the death of me