Calculus 2 : First and Second Derivatives of Functions

Study concepts, example questions & explanations for Calculus 2

varsity tutors app store varsity tutors android store

Example Questions

Example Question #41 : First And Second Derivatives Of Functions

Find the velocity given the displacement function

Possible Answers:

Correct answer:

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

Possible Answers:

Correct answer:

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

Possible Answers:

Correct answer:

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

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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

Possible Answers:

None of the other answers

Correct answer:

Explanation:

We need to use the Product Rule to evaluate the derivative here.

The formula for the Product Rule is

If , , then ,

Plugging these into our formula, we get-

Learning Tools by Varsity Tutors