# High School Math : Understanding Derivatives of Exponents

## Example Questions

### Example Question #2143 : High School Math

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 #1 : Understanding Derivatives 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

### Example Question #2 : Understanding Derivatives Of Exponents

What is  ?

Possible Answers:

Correct answer:

Explanation:

Therefore,

for any real , so , and

### Example Question #74 : Calculus I — Derivatives

What is  ?

Possible Answers:

Correct answer:

Explanation:

Therefore,

for any positive , so , and

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