Find $\frac{dy}{dx}$ for the equation $2x + 3y = \sin y$.

If the slope of a tangent to the curve $xy + ax + by = 0$ at the point $(1, 1)$ on it is $2$,then $a - b$ is

If $x \sqrt{1+y}+y \sqrt{1+x}=0$ for $-1 < x < 1$,prove that $\frac{dy}{dx} = -\frac{1}{(1+x)^2}$.

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

If the tangent to the curve $xy + ax + by = 0$ at $(1, 1)$ makes an angle of $\tan^{-1} 2$ with the positive direction of the $x$-axis, then the value of $\frac{ab}{a + b}$ is...

For the curve $C : (x^{2}+y^{2}-3)+(x^{2}-y^{2}-1)^{5}=0$,the value of $3y^{\prime}-y^{3}y^{\prime\prime}$ at the point $(\alpha, \alpha)$,where $\alpha > 0$,on $C$ is equal to: