$\cfrac { d }{ dx } \left( -\cos { 3\left( \cfrac { \pi }{ 6 } +{ x }^{ 0 } \right) } \right)$=?

If $\displaystyle \frac { \cos ^{ 4 }{ \theta } }{ x } +\frac { \sin ^{ 4 }{ \theta } }{ y } =\frac { 1 }{ x+y }$ then $\displaystyle \frac { dy }{ dx } =$

If $y=\sqrt{\dfrac{1-\sin 2x}{1+\sin 2x}}$, then $\left(\dfrac{dy}{dx}\right)_{x=0}=$

$\mathbf{g}(\mathrm{x})=\cot ^{-1} \mathrm{x}$;

d/dx of g(x)=?

Suppose $A=\displaystyle \frac{dy}{dx}$ when $x^2+y^2=4$ at $(\sqrt{2},\sqrt{2})$,$B=\displaystyle \frac{dy}{dx}$ when $\sin y+ \sin x=\sin x-\sin y$ at $(\pi,\pi)$ and $C=\displaystyle \frac{dy}{dx}$ when $2e^{xy}+e^x e^y-e^x-e^y=e^{xy+1}$ at $(1,1)$, then $(A+B+C)$ has the value equal to