Question

If x = uv, y = , then
ə (x,y)
a(u,v)
is equal to
​

Answer 1

Answer:

3ccccy the most handsome boy in the world and lowest price and lowest price.

Answer 2

Correct question: If x = uv, y = u/v , then $\frac{\partial(x,y)}{\partial(u,v)}$ is equal to

Answer:

The value of $\frac{\partial(x,y)}{\partial(u,v)}$ is $-2u/v$.

Step-by-step explanation:

Consider the equation as follows:

$x=uv$

$y=u/v$

Partial derivative of $x$ with respect to $u$.

$\frac{\partial x}{\partial u}=v$

Partial derivative of $x$ with respect to $v$.

$\frac{\partial x}{\partial v}=u$

Similarly,

Partial derivative of $y$ with respect to $u$.

$\frac{\partial y}{\partial u}=1/v$

Partial derivative of $y$ with respect to $v$.

$\frac{\partial y}{\partial v}=-u/v^2$

Then,

$\frac{\partial(x,y)}{\partial(u,v)}=\left[\begin{array}{cc}\frac{\partial x}{\partial u} &\frac{\partial x}{\partial v}&\\\frac{\partial y}{\partial u}&\frac{\partial y}{\partial v}\end{array}\right]$

$\frac{\partial(x,y)}{\partial(u,v)}=\left[\begin{array}{cc}v &u&\\1/v&\(-u/v^2\end{array}\right]$

        $=\frac{-uv}{v^2} -\frac{u}{v}$ (Determinant of a matrix)

        $=-\frac{u}{v} -\frac{u}{v}$

$\frac{\partial(x,y)}{\partial(u,v)}=-2u/v$

Therefore, $\frac{\partial(x,y)}{\partial(u,v)}$ is equal to $-2u/v$.

#SPJ3