Question

If x=u(1-v) and y=uv then del(x,y)/del(u,v)=
​

Answer 1

Step-by-step explanation:

the answer is mentioned clearly in the picture above

Answer 2

Given:

 x=u(1-v) and y=uv

To Find:

$\frac{\partial (x,y)}{\partial(u,v)}$

Step-by-step explanation:

• To solve for partial equation we will use Jacobian formula
• $\frac{\partial x}{\partial u}= 1-v+0=1-v\\\frac{\partial x}{\partial v}=u(-1)+0=-u\\\frac{\partial y}{\partial u}=v+0=v\\\frac{\partial y}{\partial u}=u+0=u$
• Then using Jacobian formula $=\left[\begin{array}{ccc}\frac{\partial x}{\partial u}&\frac{\partial x}{\partial v}\\\frac{\partial y}{\partial u}&\frac{\partial y}{\partial v}\end{array}\right]$

• after putting the values we get
• $(1-v)\times u-v\times (-u)\\=(u-u\times v)+u\times v\\=u$

The final answer is u