Let $\Gamma ( u , v , w )$ be a function of three variables with $F _ { u } + F _ { w } = - 1$ .Suppose that $G ( x , y ) = F ( x , x - y , x )$ .Simplify $G _ { x } + G _ { y }$ .
A) $G _ { x } + G _ { y } = 0$ .
B) $G _ { x } + G _ { y } = - 1$ .
C) $G _ { x } + G _ { y } = 1$ .
D) $G _ { x } + G _ { y } = - 2$ .

Question

Quizplus · Accepted Answer

Given $G(x, y) = F(x, x - y, x)$, we differentiate $G$ with respect to $x$ and $y$ using the chain rule. For $G_x$, we get $F_u + F_v \cdot (-1) + F_w$. For $G_y$, we get $F_v$. Adding $G_x$ and $G_y$ gives $F_u + F_w + F_v - F_v = F_u + F_w = -1$, as $F_u + F_w = -1$ by given condition.

Let Γ(u,v,w)\Gamma ( u , v , w )Γ(u,v,w) Be a Function of Three Variables With

Let $\Gamma ( u , v , w )$ Be a Function of Three Variables With