How do you differentiate #y=sqrt(tan^-1x)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Anees Apr 16, 2015 #dy/dx=1/(2sqrt(tan^-1x))(1/(1+x^2))# #y=sqrt(tan^-1x)# #dy/dx=1/2(tan^-1x)^((-1)/2)d/dxtan^-1x# #dy/dx=1/(2sqrt(tan^-1x))(1/(1+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 5768 views around the world You can reuse this answer Creative Commons License