If $x^2+y^2=4$, then $y \frac{dy}{dx}+x=$

If $2x^2 - 3xy + 4y^2 + 2x - 3y + 4 = 0$, then $\left(\frac{dy}{dx}\right)_{(3,2)} = $

If $\cos y = x \cos (a+y)$ with $\cos a \neq \pm 1,$ prove that $\frac{dy}{dx} = \frac{\cos^2 (a+y)}{\sin a}$.

If $x^{p}+y^{q}=(x+y)^{p+q}$,then $\frac{dy}{dx}$ is

If $x \sqrt{1+y}+y \sqrt{1+x}=0$,then $\frac{d y}{d x}$ is equal to

Let $C$ be the curve $y^3 - 3xy + 2 = 0$. If $H$ and $V$ are the sets of points on the curve $C$ where the tangent to the curve is horizontal and vertical respectively,then