Question #57682 Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Monzur R. Apr 16, 2017 See below Explanation: #y=arcsin(cot(x^-2))# #siny=cot(x^-2)# #(cosy)y'=-(2csc^2(x^-2))/x^3# #y'=-(2csc^2(x^-2))/(x^3cosy)# #cosy=+-sqrt(1-sin^2y)=+-sqrt(1-cot^2(x^-2))# #y'=+-(2csc^2(x^-2))/(x^3sqrt(1-cot^2(x^-2))) # 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 1093 views around the world You can reuse this answer Creative Commons License