Question #732ab Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer sankarankalyanam Oct 23, 2017 #y’ = 4/sqrt(x^2 - 2)# Explanation: d /(dx) (cos^-1 x) = -1/sqrt(1-x^2)# #y = cos ^-1 (2/x^2)# #:. y’ = (-1/(sqrt(1-(2/x^2))) * (-4/x))# #y’ = (4/cancel(x))(cancel(x )/ (sqrt(x^2 - 2)))# #y’ = 4 / sqrt(x^2 - 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 1082 views around the world You can reuse this answer Creative Commons License