How do you find the derivative of f(x) =(arcsin(3x))/x? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Marko T. Mar 14, 2018 The answer would be (3*sqrt(1-9x^2))/(x*(1-9x^2))-arcsin(3x)/x^2 Explanation: f(x)=arcsin(3x)/x d/dx(arcsin(3x)/x) =(d/dx(arcsin(3x))*x-d/dx(x)*arcsin(3x))/x^2 =((d/dx(3x))/sqrt(1-(3x)^2)-arcsin(3x))/x^2 =((3x)/sqrt(1-9x^2)-arcsin(3x))/x^2 =((3x)sqrt(1-9x^2))/((x^2)(1-9x^2))-arcsin(3x)/x^2 =(3sqrt(1-9x^2))/(x(1-9x^2))-arcsin(3x)/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 1844 views around the world You can reuse this answer Creative Commons License