Blog #3

SHORTCUTS! Yea, so this week we found out how to apply some derivative shortcuts. I'm one of those people who most likely will screw up the shortcuts more than the long formula, but it helps on timed tests. There are many different shortcuts. There is the constant rule, the powers rule, and many others.

The constant rule is by far the easiest of them all. It states that the derivative of any constant is 0.
Ex. Find the derivative of 10.
The answer would be zero because of the power rule.
To prove this i will plug it in to the definition of a derivative formula.

f(x-dx)-f(x)/dx

10-10/dx

0/dx

0

The other shortcut i mentioned is the power rule. This one is pretty cool. What it says is that when you have any variable with an exponent, to find the derivative you can follow these simple steps.

1) Move the exponent to the front of the equation.
2) Subtract 1 from the original exponent for the new exponent.

Ex. Find the derivative of x^4.

x^4

4x^3

The 4 moved to the front. Then I subtracted one from the original exponent(4) and got 3 as my new exponent.