First Order Partial Derivatives of a Function

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ok once again thanks Voko you have been brilliant!

[tex]f(x)= [1+(x^2+y^2)^{-1/2}(x)] [\frac{1}{x+\sqrt{x^2+y^2}} - \frac{1}{x-\sqrt{x^2+y^2}}][/tex]

So this is written correctly then?
 
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Again, the second term is incorrect. You cannot go from (-a)(b) to -(-ab), but that's what you insist on doing. (-a)(b) = -(ab).