What is the derivative of #arcsin(x^2/4)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Matt B. Nov 22, 2016 #d/dx(arcsin(x^2/4)) = x/(2sqrt(1-x^4/16))# Explanation: Let #u=x^2/4# #d/dx(arcsinu) = 1/sqrt(1-u^2) * d/dx(u)# #d/dx(u) = x/2# The rest is just plugging in and multiplying #u#. 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 1442 views around the world You can reuse this answer Creative Commons License