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

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

If $$y=\log _{10} x+\log _x 10+\log _x x+\log _{10} 10$$, then $$\frac{d y}{d x}=$$

If $$y=x \tan y$$, then $$\frac{d y}{d x}=$$