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If u=2xy, v=x2-y2 and x=rcos?, y=rsin? then find \[ \dfrac {\partial (u_1v)}{\partial (\partial_1 \theta)} \]
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written 3.0 years ago by
teamques10
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$u=2xy, v=x^2-y^2 \cdots (Given)$ $\dfrac {\delta (u,v)}{\delta (r,\theta)}= \dfrac {\delta (u,v)}{\delta (x,y)}. \dfrac {\delta (x,y)}{\delta (r,\theta)} \cdots(A)$ $\dfrac {\delta (u,v)}{\delta (x,y)}= \begin{bmatrix} \dfrac {\delta u}{\delta x} &\dfrac {\delta u}{\delta y} \[0.3em] \dfrac {\delta v}{\delta x} & \dfrac {\delta v}{\delta y} \[0.3em]
\end{bmatrix} $ $\dfrac {\delta u}{\delta x}=2y;\ \dfrac {\delta u}{\delta …
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