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))#
