Question

alguem me ajude por favor determine as derivadas parciais de primeira ordem da função f(x,y)= x-y/x+y

Answer 1

$f(x,y)= \frac{x-y}{x+y} \\\\ \frac{\partial f}{\partial x }= \frac{(x-y)'(x+y)-(x-y)(x+y)'}{(x+y)^2} = \frac{(1-0)(x+y)-(x-y)(1+0)}{(x+y)^2} = \frac{x+y-x+y}{(x+y)^2} \\\\ \boxed{\boxed{ \frac{\partial f}{\partial x }= \frac{2y}{(x+y)^2}}}\\\\\\ \frac{\partial f}{\partial y }= \frac{(x-y)'(x+y)-(x-y)(x+y)'}{(x+y)^2} = \frac{(0-1)(x+y)-(x-y)(0+1)}{(x+y)^2} = \frac{-x-y-x+y}{(x+y)^2} \\\\ \boxed{\boxed{\frac{\partial f}{\partial y }= \frac{-2x}{(x+y)^2} }}$