AP Calculus AB : Understanding the derivative of exponents

Example Questions

Example Question #51 : Finding Derivatives

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 #63 : Derivatives

What is  ?

Explanation:

Therefore,

for any real , so , and

Example Question #64 : Derivatives

What is  ?

Explanation:

Therefore,

for any positive , so , and

Example Question #1 : Understanding Derivatives Of Exponents

Give the instantaneous rate of change of the function  at .