If $(\cos x)^y=(\sin y)^x$, then $\frac{d y}{d x}$ equals

If the curves $\frac{x^2}{a}+\frac{y^2}{4}=1$ and $y^3=16 x$ intersect at right angles, then ' $a$ ' equals to

If $$y=1+\frac{x}{1 !}+\frac{x^2}{2 !}+\frac{x^3}{3 !} \ldots$$, then $$\frac{d y}{d x}$$ is equal to

The value of $$\frac{d}{d x}\left(x^n \log _a x e^x\right)$$ is