# AP Calculus AB : Understanding the derivative of trigonometric functions

## Example Questions

### Example Question #1 : Understanding The Derivative Of Trigonometric Functions

Find the derivative of the following function:       Explanation:

The derivative of is . It is probably best to memorize this fact (the proof follows from the difference quotient definition of a derivative).

Our function the factor of 3 does not change when we differentiate, therefore the answer is ### Example Question #2 : Understanding Derivatives Of Trigonometric Functions       Explanation:

The derivative of a sine function does not follow the power rule. It is one that should be memorized. .

### Example Question #1 : Specific Derivatives

What is the second derivative of ?      Explanation:

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 : Derivative Review

Find the derivative of the function .      Explanation:

We can use the Chain Rule:

Let , so that . ### Example Question #3 : Understanding Derivatives Of Trigonometric Functions

Compute the derivative of the function .      Explanation:

Use the Chain Rule.

Set and substitute.    ### All AP Calculus AB Resources 