How do you differentiate y=sqrt(tan^-1x)y=√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))dydx=12√tan−1x(11+x2) y=sqrt(tan^-1x)y=√tan−1x dy/dx=1/2(tan^-1x)^((-1)/2)d/dxtan^-1xdydx=12(tan−1x)−12ddxtan−1x dy/dx=1/(2sqrt(tan^-1x))(1/(1+x^2))dydx=12√tan−1x(11+x2) Answer link Related questions What is the derivative of f(x)=sin^-1(x)f(x)=sin−1(x) ? What is the derivative of f(x)=cos^-1(x)f(x)=cos−1(x) ? What is the derivative of f(x)=tan^-1(x)f(x)=tan−1(x) ? What is the derivative of f(x)=sec^-1(x)f(x)=sec−1(x) ? What is the derivative of f(x)=csc^-1(x)f(x)=csc−1(x) ? What is the derivative of f(x)=cot^-1(x)f(x)=cot−1(x) ? What is the derivative of f(x)=(cos^-1(x))/xf(x)=cos−1(x)x ? What is the derivative of f(x)=tan^-1(e^x)f(x)=tan−1(ex) ? What is the derivative of f(x)=cos^-1(x^3)f(x)=cos−1(x3) ? What is the derivative of f(x)=ln(sin^-1(x))f(x)=ln(sin−1(x)) ? See all questions in Differentiating Inverse Trigonometric Functions Impact of this question 6046 views around the world You can reuse this answer Creative Commons License