Question #d4611 Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Cem Sentin Oct 8, 2017 dy/dx=-2/(x^2+1) or (-2x^(-1))/[x+x^(-1)] Explanation: y=cos^(-1) [(x-x^(-1))/(x+x^(-1))] =cos^(-1) [(x^2-1)/(x^2+1)] Take cosine both sides, cosy=(x^2-1)/(x^2+1) Take differentiation both sides, -siny*dy=[2x*(x^2+1)-2x*(x^2-1)]*dx/(x^2+1)^2 -sqrt[1-(cosy)^2]*dy=(4x*dx)/(x^2+1)^2 -sqrt(1-[(x^2-1)/(x^2+1)]^2)*dy=(4x*dx)/(x^2+1)^2 -sqrt[(4x^2)/(x^2+1)^2]*dy=(4x*dx)/(x^2+1)^2 -(2x*dy)/(x^2+1)=(4x*dx)/(x^2+1)^2 dy/dx=(4x*dx)/(x^2+1)^2*-(x^2+1)/(2x) dy/dx=-2/(x^2+1) or (-2x^(-1))/[x+x^(-1)] 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 1564 views around the world You can reuse this answer Creative Commons License