AP Calculus AB : Understanding the derivative of exponents

Study concepts, example questions & explanations for AP Calculus AB

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Example Questions

Example Question #1 : Understanding The Derivative Of Exponents

Find the derivative for 

Possible Answers:

Correct answer:

Explanation:

The derivative must be computed using the product rule.  Because the derivative of  brings a  down as a coefficient, it can be combined with  to give 

Example Question #2 : Understanding The Derivative Of Exponents

What is  ?

Possible Answers:

Correct answer:

Explanation:

Therefore, 

 for any real , so , and

Example Question #3 : Understanding The Derivative Of Exponents

What is  ?

Possible Answers:

Correct answer:

Explanation:

Therefore, 

 for any positive , so , and

 

 

Example Question #4 : Understanding The Derivative Of Exponents

Give the instantaneous rate of change of the function  at .

Possible Answers:

Correct answer:

Explanation:

The instantaneous rate of change of  at  is , so we will find  and evaluate it at .

 for any positive , so 

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