SOLUTION: Differentiate ln(sqrt((x)(x)+1)-x) with respect to x.

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Question 835437: Differentiate ln(sqrt((x)(x)+1)-x) with respect to x.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let
f=ln%28sqrt%28x%5E2%2B1%29-x%29
u=sqrt%28x%5E2%2B1%29-x
f=ln%28u%29
Then,
df%2Fdx=%28df%2Fdu%29%28du%2Fdx%29
df%2Fdx=%28d%28ln%28u%29%29%2Fdu%29%28du%2Fdx%29
df%2Fdx=%281%2Fu%29%28du%2Fdx%29
.
.
.
u=%28x%5E2%2B1%29%5E%281%2F2%29-x
du%2Fdx=%281%2F2%29%28x%5E2%2B1%29%5E%28-1%2F2%29%2A%282x%29-1
du%2Fdx=x%2Fsqrt%28x%5E2%2B1%29-1
.
.
df%2Fdx=%281%2F%28sqrt%28x%5E2%2B1%29-x%29%29%2A%28x%2Fsqrt%28x%5E2%2B1%29-1%29