How do you find the derivatives of y=(lnx)^3? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Roberto G. Feb 18, 2017 dy/dx = 3((ln(x))^2/x) Explanation: We can apply Chain Rule of Differentiation. d/dx f@g(x)= [d/dx f(u)][d/dx u] or [f@g(x)]' = {f'[g(x)]}{g'(x)} Let u = lnx and f(x) = (...)^3 d/dx f@g(x) =[3(lnx)^2][d/dx lnx] d/dx f@g(x) =[3(lnx)^2][1/x] d/dx f@g(x) = 3((lnx)^2/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 2140 views around the world You can reuse this answer Creative Commons License