Find the derivative of e^{log x}

by RoRi

November 10, 2015

Find the derivative of the following function:

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

Since

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

the derivative is given by

$f'(x) = 1.$

We could check this if we wanted by using the chain rule and the derivative of the exponential on the original formula for $f(x)$ ,

$f'(x) = (\log x)' (e^{\log x}}) = \frac{1}{x} x = 1.$

Stumbling Robot