How to solve the mentioned problem?

Question

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

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Answer 1 · 2017-12-21T15:59:00

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

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)#