Answer
a) $z_x=f'(x)g(y)$
$z_y=f(x)g'(y)$
b)$z_x=f'(xy)\times y$
$z_y=f'(xy)\times x$
c) $z_x=f'(x/y)\times1/y$
$z_y=f'(x/y)\times -x/y^2$
Work Step by Step
Take the first partial derivatives of the given function. When taking partial derivative with respect to x, treat y as a constant, and vice versa. Do not forget to apply chain rule:
a) $z_x=f'(x)g(y)\times1$
$z_y=f(x)g'(y)\times1$
b)$z_x=f'(xy)\times y$
$z_y=f'(xy)\times x$
c) $z_x=f'(x/y)\times1/y$
$z_y=f'(x/y)\times -x/y^2$
