# Calculus 2 : First and Second Derivatives of Functions

## Example Questions

### Example Question #41 : First And Second Derivatives Of Functions

Find the velocity given the displacement function

Explanation:

The derivative of the displacement function is the velocity, so we need to find . We can use the power rule

with

to get

### Example Question #42 : First And Second Derivatives Of Functions

Find the velocity given the displacement function

Explanation:

The derivative of the displacement function is the velocity, so we need to find . We can use the power rule

with   along with the chain rule to get

### Example Question #43 : First And Second Derivatives Of Functions

Find the velocity given the displacement function

Explanation:

The derivative of the displacement function is the velocity, so we need to find . We can use the power rule

with   along with the chain rule to get

### Example Question #44 : First And Second Derivatives Of Functions

Find the velocity given the displacement function

Explanation:

The derivative of the displacement function is the velocity, so we need to find . We can use the power rule

with   along with the chain rule to get

### Example Question #45 : First And Second Derivatives Of Functions

Given the displacement function , find the velocity function.

Explanation:

To find the velocity of , we need to find the derivative. This can be done with the chain rule:

with  and , so we get

and

so we get

### Example Question #46 : First And Second Derivatives Of Functions

Given the displacement function , find the velocity function.

Explanation:

To find the velocity of , we need to find the derivative. This can be done with the chain rule:

with  and , so we get

and

so we get

### Example Question #47 : First And Second Derivatives Of Functions

Given the displacement function

find the velocity function.

Explanation:

To find the velocity of , we need to find the derivative. This is simply:

using the power rule:

### Example Question #48 : First And Second Derivatives Of Functions

Given the velocity function

find the acceleration function .

Explanation:

The acceleration function  can be derived from the velocity function by taking the derivative: . So we get

### Example Question #49 : First And Second Derivatives Of Functions

Given the velocity function

find the acceleration function .

Explanation:

The acceleration function  can be derived from the velocity function by taking the derivative: . So we get

### Example Question #50 : First And Second Derivatives Of Functions

Find the derivative of