Derivative of (-sqrt(1 + x^2)) / x: What Did I Do Wrong?

[PhizKid]

Homework Statement

Differentiate (-sqrt(1 + x^2)) / x

Homework Equations

[f'(x)g(x) - f(g)g'(x)] / [g(x)]^2

The Attempt at a Solution

I need to simplify it further, but before I do I checked it into Mathematica and it says the derivative is incorrect. What did I do wrong?

 

[Mark44]

What you did looks fine. It might be that what you typed into Mathematica isn't right. Or maybe Mathematica is just giving you the same thing in a different form. Try factoring (x² + 1)^-1/2 out of the two terms in the numerator.