Continuity and Differentiability — MATHS STD 12 Science — Question

$\Rightarrow \frac{d}{{dx}}{x^2} + \frac{d}{{dx}}xy + \frac{d}{{dx}}{y^2} = \frac{d}{{dx}}100$

$\Rightarrow 2x + \left( {x\frac{d}{{dx}}y + y\frac{d}{{dx}}x} \right) + 2y\frac{{dy}}{{dx}} = 0$

$ \Rightarrow 2x + x\frac{{dy}}{{dx}} + y + 2y\frac{{dy}}{{dx}} = 0$

$\Rightarrow \left( {x + 2y} \right)\frac{{dy}}{{dx}} = - 2x - y$

$ \Rightarrow \frac{{dy}}{{dx}} = \frac{{ - \left( {2x + y} \right)}}{{x + 2y}}$