Find the matrix $\mathrm{A}^2$, where $A=\left[a_{i j}\right]$ is a $2 \times 2$ matrix whose elements are given by $a_{i j}=$ maximum $(i, j)-$ minimum $(i, j)$

If $x e^y=1$, then the value of $\frac{d y}{d x}$ at $x=1$ is

Derivative of $e^{\sin ^2 x}$ with respect to $\cos x$ is

The function $f(x)=\frac{x}{2}+\frac{2}{x}$ has a local minima at $x$ equal to