Find the derivative of 2^x

by RoRi

November 9, 2015

Find the derivative of the function:

$f(x) = 2^x.$

First, using the definition of the exponential we rewrite $f(x)$ in a form we know what to do with,

$f(x) = 2^x = e^{\log (2^x)} = e^{x \log 2}.$

Then, we can take the derivative using the chain rule and the formula for the derivative of an exponential,

$f'(x) = (\log 2)\left(e^{x \log 2} \right) = (\log 2)(2^x) = 2^x \log x.$

Stumbling Robot