What is the derivative of #y=(lnx)^(cosx)#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer Manikandan S. Mar 7, 2017 Use substitution Explanation: #ln y = cos x ln(ln(x))# #1/y dy/dx = sin x ln(ln x)+cosx 1/ln(x) 1/x# #dy/dx = (ln x)^(cos x)\times (sin x ln(ln x)+cosx 1/ln(x) 1/x)# Answer link Related questions What is the derivative of #f(x)=log_b(g(x))# ? What is the derivative of #f(x)=log(x^2+x)# ? What is the derivative of #f(x)=log_4(e^x+3)# ? What is the derivative of #f(x)=x*log_5(x)# ? What is the derivative of #f(x)=e^(4x)*log(1-x)# ? What is the derivative of #f(x)=log(x)/x# ? What is the derivative of #f(x)=log_2(cos(x))# ? What is the derivative of #f(x)=log_11(tan(x))# ? What is the derivative of #f(x)=sqrt(1+log_3(x)# ? What is the derivative of #f(x)=(log_6(x))^2# ? See all questions in Differentiating Logarithmic Functions without Base e Impact of this question 4222 views around the world You can reuse this answer Creative Commons License