જો $u=\sin ^{-1}\left(\frac{x^4+y^4}{x+y}\right)$ હોય,તો $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ ની કિંમત શોધો.

જો $z = \frac{y}{x} \left[ \sin \left( \frac{x}{y} \right) + \cos \left( 1 + \frac{y}{x} \right) \right]$ હોય,તો $x \frac{\partial z}{\partial x} = $

જો $u = (x^2 + y^2 + z^2)^{3/2}$ હોય,તો $\left( \frac{\partial u}{\partial x} \right)^2 + \left( \frac{\partial u}{\partial y} \right)^2 + \left( \frac{\partial u}{\partial z} \right)^2 = $

જો $f(x, y) = \frac{\cos(x - 4y)}{\cos(x + 4y)}$ હોય,તો $\left. \frac{\partial f}{\partial x} \right|_{y = \frac{x}{2}}$ ની કિંમત શું થાય?

જો $z = \sin^{-1}\left( \frac{x+y}{\sqrt{x} + \sqrt{y}} \right)$ હોય,તો $x\frac{\partial z}{\partial x} + y\frac{\partial z}{\partial y}$ ની કિંમત શોધો.

જો $u = \frac{x + y}{x - y}$ હોય,તો $\frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} = $