# Derivative of a^{x}

How to find the derivative of the given function by using the derivative of a^{x}: formula, 1 example, and its solution.

## Formula

The derivative of a^{x}, [a^{x}]',

is a^{x} ln a.

## Exampley = 2^{2x + 1}, y' = ?

Solution

Solution (Detail)

y = 2^{2x + 1}

is a composite function of

y = 2^{(whole)} and (whole) = 2x + 1.

So the derivative of the composite function is,

the derivative of the outer function 2^{2x + 1}, 2^{2x + 1} ln 2

times,

the derivative of the inner function 2x + 1, 2.

2^{2x + 1}⋅2 = 2^{2x + 1 + 1} = 2^{2x + 2}

Product of Powers

So

2^{2x + 2} ln 2

is the derivative of 2^{2x + 1}.