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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