(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex]f(x) = ln(x+\sqrt{x^2+1})[/itex]

2. Relevant equations

3. The attempt at a solution

First, I applied the chain rule.

[itex][\frac{1}{x+\sqrt{x^2+1}}]Dx[x+\sqrt{x^2+1}][/itex]

Second, to find [itex]Dx[x+\sqrt{x^2+1}][/itex], I broke it into two derivatives. Derivative of x is 1, so

[itex]1 + Dx[\sqrt{x^2+1}][/itex]

To find [itex]Dx[\sqrt{x^2+1}][/itex], I applied the chain rule once more.

[itex][\frac{1}{2}][2x]\frac{1}{\sqrt{x^2+1}}[/itex]

I simplified this result to:

[itex]\frac{x}{\sqrt{x^2+1}}[/itex]

Leading to and end-derivative of:

[itex][\frac{1}{x+\sqrt{x^2+1}}][1+\frac{x}{\sqrt{x^2+1}}][/itex]

The book gives a much cleaner answer of [itex]\frac{1}{\sqrt{x^2+1}}[/itex]

Is my answer equivalent? If yes, how would I get to that? If no, what part of the calculus did I screw up?

WOW, Nevermind!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Another Iffy Derivative

**Physics Forums | Science Articles, Homework Help, Discussion**