Question #b7cd0 Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Shiva Prakash M V Feb 19, 2018 #dy/dx=1/(2sqrt(x(1-x)# Explanation: #"Let"y=sin^-1(sqrtx)# #dy/dx=?# #u=sqrtx# #u^2=x# #(du)/dx=1/(2sqrtx)# #y=sin^-1u# #(dy)/(du)=1/sqrt(1-u^2)# #(dy)/(du)=1/sqrt(1-x)# #dy/dx=dy/(du)(du)/dx# #dy/dx=1/sqrt(1-x)xx1/(2sqrtx)=1/(2sqrt(x(1-x)# #dy/dx=1/(2sqrt(x(1-x)# 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 1091 views around the world You can reuse this answer Creative Commons License