Question

Find the Differential of: "y = ln[sqrt.(1+x^2)]"

Any and all help is greatly appreciated!

Answer 1

I got:
\[y= \ln \sqrt{1+x^2}\]
\[dy = \frac{1}{(x^2 +1)^{1/2}}*(2x)\]
\[= \frac{2x}{(x^2+1)^{1/2}}\]
BUT... my book has:
\[\frac{x}{(x^2+1)}\]

Answer 2

Can anyone explain where I went wrong?

Answer 3

Specifically, I'm wondering where the power of 1/2 goes in the denominator. I see how I messed up the coefficient of 2 in the numerator, but where do the square roots go?

Answer 4

@freckles