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

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

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

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

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

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