How do you differentiate #f(x)= ln(1-x)^4#?

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Answer 1 · 2016-12-27T09:33:15

#(dy)/(dx)=(-4(1-x)^3)/((1-x)^4)#

#f(x)=ln(1-x)^4#

Using the chain rule.

#(dy)/(dx)=(dy)/(du)xx(du)/(dx)#

let#" "u=(1-x)^4=>(du)/(dx)=-4(1-x)^3#

#y=lnu=>(du)/(dx)=1/u#

#(dy)/(dx)=(dy)/(du)xx(du)/(dx)#

#(dy)/(dx)=1/uxx-4(1-x)^3#

#(dy)/(dx)=(-4(1-x)^3)/((1-x)^4)#