What is the derivative of f(x)=tan(1/lnx)? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer mason m Dec 6, 2015 =-(sec^2(1/lnx))/(xln^2x) Explanation: According to the chain rule: f'(x)=sec^2(1/lnx)d/dx[1/lnx] =sec^2(1/lnx)d/dx[ln^-1x] =sec^2(1/lnx)xx-ln^-2x xx d/dx[lnx] =sec^2(1/lnx)(1/-ln^2x)(1/x) =-(sec^2(1/lnx))/(xln^2x) 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 2617 views around the world You can reuse this answer Creative Commons License