# AP Calculus AB : Derivatives

## Example Questions

### Example Question #5 : Derivatives Of Functions

Find :

Explanation:

This is the product rule, which is: (derivative of the first)(second)+(derivative of the second)(first)

So:

### Example Question #6 : Derivatives Of Functions

Find the derivative of the following:

Explanation:

This is a combination of chain rule and quotient rule.

So:

Which when simplified you get:

### Example Question #7 : Derivatives Of Functions

Find the derivative of the following:

Explanation:

This problem is just addition of derivatives using trigonometric functions.

So:

### Example Question #8 : Derivatives Of Functions

Find the derivative:

Explanation:

The is a quotient rule using a trigonometric function.

So:

You can pull out an "x" and cancel it to get:

### Example Question #9 : Derivatives Of Functions

Find the derivative:

Explanation:

This is the same concept as a normal derivative just with a negative in the exponent.

which becomes:

### Example Question #10 : Derivatives Of Functions

Calculate :

Explanation:

This is a power rule that can utilize u-substitution.

So

where

So you get:

Plug "u" back in and you get:

### Example Question #21 : Ap Calculus Ab

Find the derivative of the following:

Explanation:

The easiest way to approach this problem is to break it up into terms to get:

This simplifies to:

This then becomes a simple derivative in which you get:

Which after simplifying you get:

### Example Question #12 : Derivatives Of Functions

Find the derivative:

Explanation:

This is a derivative of sums with a trigonometric function thrown in there.

Upon simplifying you get:

Keeping in mind the derivative of cos(x) is -sin(x)

### Example Question #22 : Ap Calculus Ab

Find :

Explanation:

This is a product rule using trigonometric functions:

This can be simplified further:

What is in red cancels and you get:

But you can take this one step further and pull out a sin(x) to get:

Differentiate.