derivative of ln(x*sqrt(x^2-1)) vs. derivative of ln(x+sqrt(x^2-1))

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derivative of ln(x*sqrt(x^2-)), derivative of ln(x+sqrt(x^2-1)),

This problem is from Single Variable Calculus, by James Stewart,

blackpenredpen
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big effort bro and i appreciate it
when you multiply with sqrt x^2+1 it was a magic step to solve it ♥ 6:19

muhammedg-tips
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I am confused on what you did at 4:43? Why did you do 1/2?

shadimawari