If $$y=1+x e^y$$, then $$\frac{d y}{d x}=$$

If $$x=e^t(\sin t-\cos t)$$ and $$y=e^t(\sin t+\cos t)$$, then $$\frac{d y}{d x}$$ at $$t=\frac{\pi}{3}$$ is

If $$\sin ^2 x+\cos ^2 y=1$$, then $$\frac{d y}{d x}=$$

$$ \text { If } u=\cos ^3 x, v=\sin ^3 x \text {, then }\left(\frac{d v}{d u}\right)_{x=\frac{\pi}{4}} \text { is equal to } $$