If $f(x, y) = \frac{\cos(x - 4y)}{\cos(x + 4y)}$, then $\left. \frac{\partial f}{\partial x} \right|_{y = \frac{x}{4}}$ is equal to:

If $u = u(x, y) = \sin(y + ax) - (y + ax)^2$, then which of the following is true?

If $z=\log (\tan x+\tan y)$,then $(\sin 2 x) \frac{\partial z}{\partial x}+(\sin 2 y) \frac{\partial z}{\partial y}$ is equal to

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

If $f(x, y) = \frac{\cos(x - 4y)}{\cos(x + 4y)}$,then $\left. \frac{\partial f}{\partial x} \right|_{y = \frac{x}{2}}$ is equal to:

If $z = \sin^{-1}\left( \frac{x+y}{\sqrt{x} + \sqrt{y}} \right)$,then $x\frac{\partial z}{\partial x} + y\frac{\partial z}{\partial y}$ is equal to