What is the derivative of #y=sqrt(tan^-1 x)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Konstantinos Michailidis Mar 16, 2016 It is #dy/dx=1/2*[arctanx]^(-1/2)*(d(arctanx)/dx)= 1/2*[arctanx]^(-1/2)*[1/(1+x^2)]= 1/2*[1/[sqrt(arctanx)*(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 5240 views around the world You can reuse this answer Creative Commons License