1. Compute all of the first order partial derivatives for the following functions. Simplify when reasonable.
(a) $f(x,y,z) = x^2y^3z^4 + x^5y - \pi xz^6 + \sqrt{7}y^8z$.
(b) $g(x,y) = \sin(xe^{x^2y})$.
(c) $h(x,y) = \frac{x-y}{\sqrt{x^2+y^2}}$.
(d) $F(x,y,z) = x^2\cos(xy + 2xz - 3yz)$.
(e) $G(x,y) = e^{\left(\frac{x^2-2y^2}{x^2+y^2}\right)}$.
(f) $H(x,y) = y^2\ln(1 + xe^{x^2y^2})$.
(g) $\phi(x,y) = \tan(x-y)$.
(h) $\Phi(w,x,y,z) = \sin(wy^3 - x^2z^4)e^{w-z}$.
