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

1 Answer
Sep 14, 2014

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

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(x)*g(x)

y'=f(x)*g'(x)+f'(x)*g(x)

Similarly following for the given problem,

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

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