Question

Hallar Derivales parciales de: Z = ara sem$\sqrt{ \frac{x-y}{x} }$

Answer 1

Sólo derivas respecto a cada variable dejando a la otra variable constante:
$f(x,y)= \sqrt{ \frac{x-y}{x} } =( \frac{x-y}{x} )^{1/2}\\ \\ \frac{\partial f}{\partial x} = \frac{1}{2} ( \frac{x-y}{x} )^{-1/2}( \frac{y}{x^2}) \\ \\ \frac{\partial f}{\partial y}= \frac{1}{2}( \frac{x-y}{x} )^{-1/2} (- \frac{1}{x} )$

Saludos!