How do you find the derivative of f(x) = x/(1-ln(x-1))?

1 Answer
Jim G.
Jul 3, 2017

f'(x)=(ln(x-1)+x/(x-1))/(2ln(x-1))

Explanation:

"differentiate using "color(blue)"quotient rule"

"given " f(x)=(g(x))/(h(x))" then"

f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr" quotient rule"

g(x)=xrArrg'(x)=1

h(x)=1-ln(x-1)rArrh'(x)=-1/(x-1)larr" chain rule"

rArrf'(x)=(1-ln(x-1)--1/(x-1))/(1-ln(x-1))^2

color(white)(rArrf'(x))=(1-ln(x-1)+1/(x-1))/(1-ln(x-1))^2

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