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

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 $$\frac{d y}{d x}=$$

The derivative of the function $$\cot ^{-1}\left[(\cos 2 x)^{1 / 2}\right]$$ at $$x=\pi / 6$$ is