Find the differentiation of y=cos^-1(ax)? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer maganbhai P. Apr 27, 2018 #y=cos^-1(ax)=>(dy)/(dx)=-1/sqrt(1-(ax)^2)d/(dx)(ax)# #(dy)/(dx)=-1/sqrt(1-a^2x^2)xxa=(-a)/sqrt(1-a^2x^2)# Note: #color(red)(d/(dX)(cos^-1X)=-1/sqrt(1-X^2)# Explanation: Here, #y=cos^-1(ax)# Let, #u=ax=>(du)/(dx)=a# #So, y=cos^-1u=>(dy)/(du)=-1/sqrt(1-u^2)# #"Using "color(blue)"Chain Rule"#, #color(blue)((dy)/(dx)=(dy)/(du)*(du)/(dx)# #:.(dy)/(dx)=-1/sqrt(1-u^2)xxa=(-a)/sqrt(1-u^2),where, u=ax# #=>(dy)/(dx)=(-a)/sqrt(1-(ax)^2)# #=>(dy)/(dx)=(-a)/sqrt(1-a^2x^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 4909 views around the world You can reuse this answer Creative Commons License