High School Math : Understanding Derivatives of Exponents

Example Questions

Example Question #1 : Understanding The Derivative Of Exponents

Find the derivative for

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 #4 : Understanding The Derivative Of Exponents

Give the instantaneous rate of change of the function  at .

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 The Derivative Of Exponents

What is  ?

Explanation:

Therefore,

for any real , so , and

What is  ?