How to solve the mentioned problem?

d/(dx)(ln(x-sqrt(x^2-1)))=?

1 Answer
Dec 21, 2017

d/dx ln(x-sqrt(x^2-1)) =-1/sqrt(x^2-1)

Explanation:

Using the chain rule:

d/dx ln(x-sqrt(x^2-1)) = 1/(x-sqrt(x^2-1)) d/dx (x-sqrt(x^2-1))

d/dx ln(x-sqrt(x^2-1)) = 1/(x-sqrt(x^2-1)) (1-x/sqrt(x^2-1))

d/dx ln(x-sqrt(x^2-1)) = 1/(x-sqrt(x^2-1)) (sqrt(x^2-1)-x)/sqrt(x^2-1)

d/dx ln(x-sqrt(x^2-1)) =-1/sqrt(x^2-1)