Find the indicated partial derivatives of $f(x,y) = 3x^{3}y^{2}$ using the limit definition. The limits need to be reduced as much as possible before they are evaluated.

$\displaystyle f_x(x,y) = \lim_{h \to 0} \frac{f(x+h,y)-f(x,y)}{h} = \lim_{h \to 0} \Bigg($ $\Bigg) =$ .

$\displaystyle f_y(x,y) = \lim_{h \to 0} \frac{f(x,y+h)-f(x,y)}{h} = \lim_{h \to 0} \Bigg($ $\Bigg) =$ .