TITLE: partial differential equation
QUESTION [1 upvotes]: $$f(x,y) = \frac 1 {\sqrt{xy}} \cdot g\left( \frac x y \right)$$
$$x>0 , y >0$$
$$x\frac {\partial f} {\partial x} +y\frac {\partial f} {\partial y}+f =0$$
Am asked to show that f solves the partial differential equation.
How to take the partial derivative of the product of 2 functions each depends on two variables ? 
I hope I was clear about the difficulty I have , thanks in advance

REPLY [0 votes]: Partial derivative of a product is the same as with differentiating a product except you do with respect to the specified variable. For example:
$(fg)_x = f_x g + f g_x$
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