Question

If x cos y + y sin x =1, then find dy
/dx​

Answer 1

$x \cos(y) + y \sin(x) = 1 \\ \frac{dy}{dx} =\cos(y) \times \frac{dy}{dx} - x \sin(y) + \sin(x) \times \frac{dy}{dx} + y \cos(x) \\ = > \frac{dy}{dx} = \frac{dy}{dx} ( \cos(y) + \sin(x) ) + y \cos(x) - x \sin(y) \\ = > \frac{dy}{dx} (1 - \cos(y) - \sin(x) = y \cos(x) - x \sin(y) \\ \frac{dy}{dx} = \frac{y \cos(x) - x \sin(y)}{1 - \cos(y) - \sin(x)}$