AP Calculus AB : Derivatives

Study concepts, example questions & explanations for AP Calculus AB

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Example Questions

Example Question #41 : Derivatives Of Functions

Given the function , find its derivative.

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

Explanation:

Use the power rule to find the derivative.

Thus, the derivative is .

Example Question #46 : Derivatives Of Functions

Find the derivative.

Possible Answers:

Correct answer:

Explanation:

Use the power rule to find the derivative.

 

Thus, the derivative is 

Example Question #51 : Derivatives Of Functions

Find the derivative.

Possible Answers:

Correct answer:

Explanation:

Use the power rule to find the derivative.

 

Example Question #52 : Derivatives Of Functions

Find the derivative.

Possible Answers:

Correct answer:

Explanation:

The derivative of  is . (Memorization)

Example Question #53 : Derivatives Of Functions

Find the derivative.

Possible Answers:

Correct answer:

Explanation:

Use the chain rule to find the derivative: 

 

Thus, .

Example Question #54 : Derivatives Of Functions

Find the derivative.

Possible Answers:

Correct answer:

Explanation:

Use the power rule to find the derivative.

The derivative of a constant is zero. 

Thus, the derivative is .

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