List of top Engineering Mathematics Questions on Partial derivatives asked in TS PGECET

If \[ \vec{v}=(x+y+1)\hat{i}+\hat{j}+(-x-y)\hat{k}, \] then the value of \[ \vec{v}\cdot(\nabla\times\vec{v}) \] is

If \(u=\sin^{-1}\left(\dfrac{x^{1/3}+y^{1/3}}{x^{1/2}-y^{1/2}}\right)^{1/2}\), then \(x\dfrac{\partial u}{\partial x}+y\dfrac{\partial u}{\partial y}=\)

If \(u = \sin^{-1}\left(\frac{x}{y}\right) + \tan^{-1}\left(\frac{y}{x}\right)\), then the value of \( x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \) is: