What is the derivative of #f(x)=e^(4x)*ln(1-x)# ?
1 Answer
Aug 27, 2014
#y'=e^(4x)(4ln(1-x)-1/(1-x))# Explanation:
#f(x)=e^(4x)⋅ln(1−x)# Suppose,
#y=f(x)*g(x)# In general Product Rule is,
#y'=f(x)*g'(x)+f'(x)*g(x)# Assume,
#f(x)=e^(4x)# and#g(x)=ln(1-x)# differentiating these functions with respect to
#x# , we get
#f'(x)=4*e^(4x)# and
#g'(x)=-1/(1-x)# Plugging these in product rule definition yields,
#y'=e^(4x)(-1/(1-x))+(4*e^(4x))ln(1-x)#
#y'=e^(4x)(4ln(1-x)-1/(1-x))#
