In #4-11, find the first partial derivatives of the function.
4. $f(x, y) = x^3e^{-3y}$
5. $z = \frac{2x - y}{x + 3y}$
6. $f(x, y) = sin^3 2x + cos^2 3y$
7. $z = ln(3x^2 + 5y^4)$
8. $f(u, v, w) = ue^v + ve^w + we^u$
9. $f(x, y) = \int_y^x (4t + 5)dt + \int_x^y \sqrt{t^2 - 2}dt$
10. $u = x^{y/(y+z)}$
11. $f(x, t) = arctan(x\sqrt{t})$
