What is the derivative of this function #y=cos^-1(2x+1)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Shwetank Mauria Nov 7, 2016 #(dy)/(dx)=-2/sqrt(1-(2x+1)^2)# Explanation: As #y=cos^(-1)(2x+1)#, we have #cosy=2x+1# and differentiating it using chain rule, we get #-siny xx (dy)/(dx)=2# or #(dy)/(dx)=-2/siny=-2/sqrt(1-cos^2y)=-2/sqrt(1-(2x+1)^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 12444 views around the world You can reuse this answer Creative Commons License