SOLUTION: find the derivative. 1. G(x) = xln(x + sqaure root of quantity 1 + x^2)

SOLUTION: find the derivative. 1. G(x) = xln(x + sqaure root of quantity 1 + x^2) - square root of quantity 1 + x^2

Question 180822: find the derivative.
1. G(x) = xln(x + sqaure root of quantity 1 + x^2) - square root of quantity 1 + x^2
Answer by user_dude2008(1862) (Show Source): You can put this solution on YOUR website!
g(x) = xln(x + sqrt(1 + x^2)) - sqrt(1 + x^2)

Let z=sqrt(1 + x^2) ----> z'=x/(sqrt(1+x^2))

g(x) = xln(x + z) - z

g'(x) = (x*z')/(x + z) - ln(x+z) - z'

g'(x) = (x*(x/(sqrt(1+x^2))))/(x + sqrt(1 + x^2)) - ln(x+sqrt(1+x^2)) - x/(sqrt(1+x^2))

g'(x) = ln(x+sqrt(1+x^2))
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