What is the derivative of this function #y=sec^-1(5x)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer maganbhai P. May 5, 2018 #(dy)/(dx)=1/(|x|sqrt(25x^2-1))# Explanation: We know that, #color(red)(d/(dt)(sec^-1t)=1/(|t|sqrt(t^2-1))# Here, #y=sec^-1(5x)# Let. #y=sec^-1u ,where, u=5x# #=>(dy)/(du)=1/(|u|sqrt(u^2-1)) and (du)/(dx)=5# #"Using "color(blue)"Integration by Parts"# #color(blue)((dy)/(dx)=(dy)/(du)*(du)/(dx)# So,#(dy)/(dx)=1/(|u|sqrt(u^2-1))xx5# #(dy)/(dx)=5/(|5x|sqrt(25x^2-1))# #(dy)/(dx)=1/(|x|sqrt(25x^2-1))# 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 7298 views around the world You can reuse this answer Creative Commons License