Continuity and Differentiability — Maths STD 12 Science — Question

$\Rightarrow \frac{d}{{dx}}\left( {xy} \right) + \frac{d}{{dx}}\left( {{y^2}} \right) = \frac{d}{{dx}}\tan x + \frac{d}{{dx}}y$

$\Rightarrow x\frac{dy}{{dx}} + y.1 + 2y\frac{dy}{{dx}} = {\sec ^2}x + \frac{dy}{{dx}}$ [By Product Rule]

$\Rightarrow x\frac{dy}{{dx}} + 2y\frac{{dy}}{{dx}} - \frac{{dy}}{{dx}} = {\sec ^2}x - y$

$$$\Rightarrow \left( {x + 2y - 1} \right)\frac{{dy}}{{dx}} = {\sec ^2}x - y$

$$$\Rightarrow \frac{{dy}}{{dx}} = \frac{{{{\sec }^2}x - y}}{{x + 2y - 1}}$