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

Given a curve $y=7 x-x^3$ and $x$ increases at the rate of 2 units per second. The rate at which the slope of the curve is changing, when $x=5$ is