第6章 6.5

(1)

$u = \frac{x+y}{z}$

$u_x = \frac{1}{z} \qquad u_y = \frac{1}{z} \qquad u_z = \frac{-(x+y)}{z^2}$

(2)

$u = \sin xyz$

$u_x = yz \cdot \cos xyz \qquad u_y = xz \cdot \cos xyz \qquad u_z = xy \cdot \cos xyz$

(3)

$u = y\log(x^2+z^2)$

$u_x = \frac{2xy}{x^2+z^2} \qquad u_y = \log(x^2+z^2) \qquad u_z = \frac{2yz}{x^2+z^2}$

(4)

$u = (ax+by+cz)^2$

$u_x = 2a(ax+by+cz) \qquad u_y = 2b(ax+by+cz) \qquad u_z = 2c(ax+by+cz)$