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if u=x^2,v=y^2 then d(u,v)/d(x,y) |
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Answer» \(\frac{d(u,v)}{d(x,y)}\) \(=\begin{vmatrix}\partial u/\partial x&\partial v/\partial x\\\partial u/\partial y&\partial v/\partial y\end{vmatrix}\) \(=\begin{vmatrix}\frac\partial{\partial x}x^2&\frac{\partial y^2}{\partial x}\\\frac{\partial}{\partial y}x^2&\frac{\partial y^2}{\partial y}\end{vmatrix}\) \(=\begin{vmatrix}2x&0\\0&2y\end{vmatrix}\) = 4xy - 0 = 4xy. |
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