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I want to solve $\displaystyle f_1(x,y)$ where $f(x,y)= \dfrac{x}{x^2+y^2}$ by hand.

What steps are involved?

Update: $\displaystyle f_1(x,y)$ denotes $\dfrac{\partial}{\partial x}f(x,y)$

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    @DavidMitra thanks again updated my question2012-09-27

2 Answers 2

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You use the quotient rule to get $\left(\frac x{x^2+y^2}\right)'=\frac {x'(x^2+y^2)-(x^2+y^2)'x}{(x^2+y^2)^2}$ then take the indicated derivatives in the numerator.

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    Thanks I solved it beautifully with the quotient rule.2012-09-27
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Treat $y$ like a constant and use quotient rule to derive with respect to $x$. Same idea for deriving with respect to $y$.