All AP Calculus AB Resources
Example Question #4 : Specific Derivatives
Find the derivative of the following function:
The derivative of is. It is probably best to memorize this fact (the proof follows from the difference quotient definition of a derivative).
the factor of 3 does not change when we differentiate, therefore the answer is
Example Question #5 : Specific Derivatives
The derivative of a sine function does not follow the power rule. It is one that should be memorized.
Example Question #6 : Specific Derivatives
What is the second derivative of ?
The derivatives of trig functions must be memorized. The first derivative is:
To find the second derivative, we take the derivative of our result.
Therefore, the second derivative will be .
Example Question #1 : Derivatives
Find the derivative of the function
We can use the Chain Rule:
Let , so that .
Example Question #7 : Specific Derivatives
Compute the derivative of the function .
Use the Chain Rule.
Set and substitute.