How do you find the derivative of arcsin((2x)/(1+x^2))? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Monzur R. Jan 24, 2017 dy/dx=1/sqrt(1-(4x^2)/(x^2+1)^2 Explanation: y=sin^-1((2x)/(x^2+1)) siny=(2x)/(1+x^2) dy/dx=1/(dx/dy) dx/dy=cosy dy/dx=1/cosy sin^2y+cos^2y=1 cos^2y=1-sin^2y cosy=sqrt(1-sin^2y)=sqrt(1-(4x^2)/(x^2+1)^2 dy/dx=1/sqrt(1-(4x^2)/(x^2+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 2080 views around the world You can reuse this answer Creative Commons License