Use the definition of partial derivatives as limits (4) to find $f_x(x,y)$, $f_y(x,y)$
Matthew Martinez 
I'm not sure how I'm supposed to approach this. I tried using the limit definition below, and then plugging in small values near 0 for h and it seemed like it would be 1.. but I think I'm way off. I know how to take partial derivatives with respect to x, y the regular way but I'm confused on how to do this with (4). I checked in my book, but it's not really straight forward. I couldn't find a similar example online either. Please help.
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$\begingroup$In each of these problems, the idea is to simplify the difference quotient so that the denominator does not tend to zero as $h\to 0$.
For instance, let $f(x,y) = x^2y$. This is not your problem, but once you understand this problem, you will know how to do your problems. Then
\begin{align*} f_x(x,y) &= \lim_{h\to 0} \frac{f(x+h,y) - f(x,y)}{h} \\&= \lim_{h\to 0} \frac{(x+h)^2y - x^2y}{h} \\&= \lim_{h\to 0} \frac{(x^2+2xh+h^2)y - x^2y}{h} \\&= \lim_{h\to 0} \frac{x^2y+2xhy+h^2y - x^2y}{h} \\&= \lim_{h\to 0} \frac{2xhy+h^2y}{h} \\&= \lim_{h\to 0} (2xy+hy) = 2xy \end{align*}
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