Please help me solve this question?

To calculate a partial derivative, such as the first partial derivative with repsect to x, call it:

delta-f(x,y)/delta-x

one differentiates with repect to x and treats y as a constant.

so, differentiate the function above as if y were, say, the number "2", using the quotient rule of calculus. Or, as I prefer, the product rule (of which the quotient rule is a special case):

d/dx (h(x)*g(x)) = h'*g + h*g'

where h(x) = xy +x^2 and g(x) = 1/(x^2 + y^2),

The rest is plug & chug, with some special care needing to be taken at the origin (0,0). That special care, in essence, asks you to think of how the function behaves as it APPROACHES (0, 0), because one cannot plug the point (0, 0) into the formula without dividing by zero.

see http://search.yahoo.com/search?p=f%28x%2Cy%29+%3D+...

hope that helps