Derivative of ax

How to find the derivative of the given function by using the derivative of ax: formula, 1 example, and its solution.

Formula

Formula

The derivative of ax, [ax]',
is ax ln a.

Example

Example

Solution

y = 22x + 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 22x + 1, 22x + 1 ln 2
times,
the derivative of the inner function 2x + 1, 2.

22x + 1⋅2 = 22x + 1 + 1 = 22x + 2

Product of Powers

So 22x + 2 ln 2 is the derivative of 22x + 1.