what is the Differentiation of (sec-1x)^2 ?

1 Answer
Feb 17, 2018

#dy/dx=(2sec^-1(x))/(x^2sqrt(1-x^-2))#

Explanation:

We want to find the derivative of

#y=(sec^-1(x))^2#

Use the Chain Rule if #y=f(g(x))=f(u)#

then #dy/dx=dy/(du)*(du)/dx#

Let #y=u^2# so that #u=sec^-1(x)#

Then #dy/(du)=2u# and #(du)/dx=1/(x^2sqrt(1-x^-2))#*

*Optionally see explanation

Apply the Chain Rule

#dy/dx=2u1/(x^2sqrt(1-x^-2))#

Substitute #u=sec^-1(x)#

#dy/dx=2sec^-1(x)1/(x^2sqrt(1-x^-2))#