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))