第6章 6.10

(1)

$z = xye^{xy}$

$z_x = ye^{xy} + xy^2 e^{xy} \qquad z_y = xe^{xy} + x^2 ye^{xy}$

(2)

$z = \log_y x = \frac{\log x}{\log y}$

$z_x = \frac{1}{x\log y} \qquad z_y = \frac{-\log x}{y(\log y)^2}$

(3)

$z = x^2\sqrt{1-y^2}$

$z_x = 2x\sqrt{1-y^2} \qquad z_y = \frac{-x^2 y}{\sqrt{1-y^2}}$

(4)

$z = \log(\sin x + \cos y)$

$z_x = \frac{\cos x}{\sin x + \cos y} \qquad z_y = \frac{-\sin y}{\sin x + \cos y}$