Let $x = u + 3$ and $y = v - 4 .$ Then $\frac { \partial ( x , y ) } { \partial ( u , v ) }$ is

A) $w$
B)1
C) $u$
D) $v$
E) $- w$

Question

Let $x = u + 3$ and $y = v - 4 .$ Then $\frac { \partial ( x , y ) } { \partial ( u , v ) }$ is

A) $w$
B)1
C) $u$
D) $v$
E) $- w$

Quizplus · Accepted Answer

The Jacobian determinant $\frac { \partial ( x , y ) } { \partial ( u , v ) }$ is calculated as the determinant of the matrix formed by the partial derivatives $\frac{\partial x}{\partial u}, \frac{\partial x}{\partial v}, \frac{\partial y}{\partial u}, \frac{\partial y}{\partial v}$. Given $x = u + 3$ and $y = v - 4$, we have $\frac{\partial x}{\partial u} = 1$, $\frac{\partial x}{\partial v} = 0$, $\frac{\partial y}{\partial u} = 0$, and $\frac{\partial y}{\partial v} = 1$. Thus, the Jacobian determinant is $1*1 - 0*0 = 1$.

Let x=u+3x = u + 3x=u+3 And y=v−4.y = v - 4 .y=v−4.

Let $x = u + 3$ And $y = v - 4 .$