What is the derivative of this function #y=cot^-1(sqrt(x-1))#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer maganbhai P. Aug 9, 2018 #(dy)/(dx)=-1/(2xsqrt(x-1))# Explanation: Here , #y=cot^-1(sqrt(x-1))# Let , #y=cot^-1u and u=sqrt(x-1)# #:.(dy)/(du)=-1/(1+u^2) and (du)/(dx)=1/(2sqrt(x-1)# Using Chain Rule: #color(blue)((dy)/(dx)=(dy)/(du)(du)/(dx)# #:.(dy)/(dx)=(-1)/(1+u^2)*1/(2sqrt(x-1))# Subst. #u=sqrt(x-1)# #:.(dy)/(dx)=-1/(1+(sqrt(x-1))^2) xx1/(2sqrt(x-1))# #:.(dy)/(dx)=-1/(1+x-1)xx1/(2sqrt(x-1))# #:.(dy)/(dx)=-1/(2xsqrt(x-1))# 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 8267 views around the world You can reuse this answer Creative Commons License