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

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The discussion focuses on differentiating the function (-sqrt(1 + x^2)) / x. The user attempted to apply the quotient rule but received an incorrect result from Mathematica. Responses suggest that the user's differentiation process appears correct, but the issue may lie in the input to Mathematica or its output being a different form. A recommendation is made to factor (x^2 + 1)^(-1/2) from the numerator to simplify the expression. The conversation emphasizes the importance of verifying both the differentiation process and the software input.
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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


NW7c8.png


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?
 
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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.
 

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