# Find the Jacobian of the transformation. x=u+4v , y=u^2-2v

Find the Jacobian of the transformation
$x=u+4v,y={u}^{2}-2v$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Brittany Patton

Basic information:
given:
$x=u+4v$
$y={u}^{2}-2v$

$\frac{\partial x}{\partial u}=\frac{\partial }{\partial u}\left(u+4v\right)=u$
$\frac{\partial y}{\partial u}=\frac{\partial }{\partial u}\left({u}^{2}-2v\right)=2u$
we thear v as command.
$\frac{\partial x}{\partial v}=\frac{\partial }{\partial v}\left(u+4v\right)=4$
$\frac{\partial y}{\partial v}=\frac{\partial }{\partial v}\left({u}^{2}-2v\right)=-2$
we thear u as command.
Calculation of Jacobian
Now, $\frac{\partial x}{\partial u}=1,\frac{\partial x}{\partial v}=4$
$\frac{\partial y}{\partial u}=2u,\frac{\partial y}{\partial v}=-2$

$=\left(-2\right)\left(1\right)-\left(4\right)\left(2u\right)$
$=-8u-2$