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 $$f(x)=[x]$$, where $$[x]$$ denotes the greatest integer less than or equal to $$x$$, is continuous at:

If $$x=A \cos 4 t+B \sin 4 t$$, then $$\frac{d^2 x}{d t^2}$$ is equal to: