What is the derivative of #f(x) = ln(cosx))#? Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer Shwetank Mauria Mar 21, 2018 #(df)/(dx)=-tanx# Explanation: We have #f(x)=ln(cosx)#, let #g(x)=cosx#, then #f(x)=ln(g(x))# Now using chain formula #(df)/(dx)=(df)/(dg(x))*(dg(x))/dx# = #1/(g(x))*(-sinx)# = #1/cosx*(-sinx)# = #-tanx# Answer link Related questions What is the derivative of #y=cos(x)# ? What is the derivative of #y=tan(x)# ? How do you find the 108th derivative of #y=cos(x)# ? How do you find the derivative of #y=cos(x)# from first principle? How do you find the derivative of #y=cos(x^2)# ? How do you find the derivative of #y=e^x cos(x)# ? How do you find the derivative of #y=x^cos(x)#? How do you find the second derivative of #y=cos(x^2)# ? How do you find the 50th derivative of #y=cos(x)# ? How do you find the derivative of #y=cos(x^2)# ? See all questions in Derivative Rules for y=cos(x) and y=tan(x) Impact of this question 5002 views around the world You can reuse this answer Creative Commons License