$u=2xy, v=x^2-y^2 \cdots (Given)$ $\dfrac {\delta (u,v)}{\delta (r,\theta)}= \dfrac {\delta (u,v)}{\delta (x,y)}. \dfrac {\delta (x,y)}{\delta (r,\theta)} \cdots(A)$ $\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 …