# AP Calculus AB : Derivatives

## Example Questions

### Example Question #41 : Derivatives Of Functions

Given the function , find its derivative.

Explanation:

Given the function , we can find its derivative using the power rule, which states that

So we have

### Example Question #42 : Derivatives Of Functions

Given the function , find its derivative.

Explanation:

Given the function , we can find its derivative using the power rule, which states that

So we have

### Example Question #41 : Computation Of The Derivative

Given the function , find its derivative.

Explanation:

Given the function , we can find its derivative using the power rule, which states that

So we have

### Example Question #42 : Derivatives Of Functions

Find the first derivative of the function:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

### Example Question #45 : Derivatives Of Functions

Find the derivative.

Explanation:

Use the power rule to find the derivative.

Thus, the derivative is .

### Example Question #46 : Derivatives Of Functions

Find the derivative.

Explanation:

Use the power rule to find the derivative.

Thus, the derivative is

### Example Question #51 : Derivatives Of Functions

Find the derivative.

Explanation:

Use the power rule to find the derivative.

### Example Question #52 : Derivatives Of Functions

Find the derivative.

Explanation:

The derivative of  is . (Memorization)

### Example Question #53 : Derivatives Of Functions

Find the derivative.

Explanation:

Use the chain rule to find the derivative:

Thus, .

### Example Question #54 : Derivatives Of Functions

Find the derivative.