How do you differentiate #y=cosln4x^3#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Bdub Oct 31, 2016 #dy/dx=(-3sin(ln(4x^3)))/x# Explanation: #y=cosln4x^3# Use chain rule #(f(g(x))' = f'(g(x)) * g'(x)# #dy/dx=-sin(ln(4x^3))*1/(4x^3) *12x^2# #dy/dx=-sin(ln(4x^3)) *3/x# #dy/dx=(-3sin(ln(4x^3)))/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 1814 views around the world You can reuse this answer Creative Commons License