What is the derivative of ln(lnx^2)? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer iceman Mar 15, 2016 d/dx [ln(lnx^2)] = 1/[xln(x)] Explanation: y = ln(lnx^2) Using the chain rule: d/dx[ln(f(x)] = [lnf(x)]^' = [1/f(x)]f'(x) dy/dx = [1/(lnx^2)] (lnx^2)^' = [1/(lnx^2)] (1/x^2)(x^2)^' =[1/(lnx^2)] (1/x^2)(2x) =2/[xln(x^2)] => simplifying: =1/[xln(x)] 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 10359 views around the world You can reuse this answer Creative Commons License