# What is the derivative of f(x)=e^(4x)*log(1-x) ?

Sep 14, 2014

$f ' \left(x\right) = {e}^{4 x} / \ln 10 \left(4 \ln \left(1 - x\right) - \frac{1}{1 - x}\right)$

Explanation :

f(x)=e^(4x)⋅log(1−x)

Converting from base $10$ to $e$

f(x)=e^(4x)⋅ln(1−x)/ln10

Using Product Rule, which is

$y = f \left(x\right) \cdot g \left(x\right)$

$y ' = f \left(x\right) \cdot g ' \left(x\right) + f ' \left(x\right) \cdot g \left(x\right)$

Similarly following for the given problem,

f'(x)=e^(4x)/ln10*1/(1-x)(-1)+ln(1−x)/ln10*e^(4x)*(4)

$f ' \left(x\right) = {e}^{4 x} / \ln 10 \left(4 \ln \left(1 - x\right) - \frac{1}{1 - x}\right)$