How do you differentiate #y=arcsin(x/2)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer sjc Oct 11, 2016 #dy/dx=1/(sqrt(4-x^2)# Explanation: #y=sin^-1(x/2)# #=>x/2=siny# #x=2siny# differentiate wrt # y# #dx/dy=2cosy# #=> dy/dx=1/(2cosy) # #dy/dx=1/(2sqrt(1-sin^2y))# #dy/dx=1/(2sqrt(1-(x/2)^2))# #dy/dx=1/(2sqrt(1-x^2/4))# #dy/dx=1/(2sqrt((4-x^2)/4))# #dy/dx=1/(2/sqrt4 sqrt((4-x^2)))# #dy/dx=1/( sqrt((4-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 1464 views around the world You can reuse this answer Creative Commons License