How do you differentiate f(x) = x/(1-ln(x-1))? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Mr. Mike Apr 12, 2018 f'(x)=(1-ln(x-1)+1/(x-1))/(1-ln(x-1))^2 Explanation: Use the quotient rule (d(g(x))/(h(x)))/(dx)=(g'(x)h(x)-g(x)h'(x))/(h(x))^2 Here g(x)=x g'(x)=1 h(x)=1-ln(x-1), and h'(x)=-1/(x-1) So f'(x)=(1-ln(x-1)-(1)(-1/(x-1)))/(1-ln(x-1))^2 f'(x)=(1-ln(x-1)+1/(x-1))/(1-ln(x-1))^2 Answer link Related questions What is the derivative of f(x)=ln(g(x)) ? What is the derivative of f(x)=ln(x^2+x) ? What is the derivative of f(x)=ln(e^x+3) ? What is the derivative of f(x)=x*ln(x) ? What is the derivative of f(x)=e^(4x)*ln(1-x) ? What is the derivative of f(x)=ln(x)/x ? What is the derivative of f(x)=ln(cos(x)) ? What is the derivative of f(x)=ln(tan(x)) ? What is the derivative of f(x)=sqrt(1+ln(x) ? What is the derivative of f(x)=(ln(x))^2 ? See all questions in Differentiating Logarithmic Functions with Base e Impact of this question 1464 views around the world You can reuse this answer Creative Commons License