How do you find the derivative of Inverse trig function y = arc csc (x/2)? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Joel Kindiak Aug 16, 2015 2/ (x^2 sin x) Explanation: y=arc csc (x/2) csc y = x/2 1/(cos y) = x/2 cos y = 2/x Diff wrt x on both sides: -sin y dy/dx = -2/x^2 dy/dx = 2/ (x^2 sin y) d/dx arc csc (x/2) = 2/ (x^2 sin y) 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 2467 views around the world You can reuse this answer Creative Commons License