I have

$\displaystyle x^2\ln(xy+4)$

$\displaystyle f_x = 2x\ln(xy+4)+\frac{x^2y}{xy+4}$

Thats correct i think but this next one im confused about.

$\displaystyle f_y = 2x\ln(xy+4)+\frac{xy^2}{xy+4}$

Is that correct , if not can someone explain to me how to differentiate that function with respect to y?