What is the derivative of (arcsin(3x))/x? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Tiago Hands Apr 23, 2015 You can solve this problem by using the quotient rule . y=(arcsin(3x))/x=u/v u=arcsin(3x) sinu=3x cosu*(du)/(dx)=3 (du)/(dx)=3/cosu=3/sqrt(1-9x^2) v=x, (dv)/(dx)=1 (dy)/(dx)=(x*3/sqrt(1-9x^2)-arcsin(3x)*1)/x^2 (dy)/(dx)=1/(x^2)*{(3x)/sqrt(1-9x^2)-arcsin(3x)} 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 6332 views around the world You can reuse this answer Creative Commons License