How do you find the derivatives of inverse function #f(x) = arctan(cos(3x))#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Truong-Son N. Jun 17, 2015 #d/(dx)[arctan(u(v(x)))] = 1/(1+u^2)*((du)/(dv))((dv)/(dx))# #d/(dx)[cosu] = -sinu*((du)/(dx))# With #u(v) = cosv# and #v(x) = 3x#: #d/(dx)[arctan(cos3x)] = 1/(1+cos^2(3x))*-sin(3x)*3# #= (-3sin3x)/(1+cos^2(3x))# Answer link Related questions What is the derivative of #f(x)=sin^-1(x)# ? What is the derivative of #f(x)=cos^-1(x)# ? What is the derivative of #f(x)=tan^-1(x)# ? What is the derivative of #f(x)=sec^-1(x)# ? What is the derivative of #f(x)=csc^-1(x)# ? What is the derivative of #f(x)=cot^-1(x)# ? What is the derivative of #f(x)=(cos^-1(x))/x# ? What is the derivative of #f(x)=tan^-1(e^x)# ? What is the derivative of #f(x)=cos^-1(x^3)# ? What is the derivative of #f(x)=ln(sin^-1(x))# ? See all questions in Differentiating Inverse Trigonometric Functions Impact of this question 1594 views around the world You can reuse this answer Creative Commons License