What is the derivative of x sin y + y cos x = 1?

Dec 30, 2016

$y ' = \frac{y \sin x - \sin y}{x \cos y + \cos x}$

Explanation:

Differentiate the equation with respect to $x$:

$\frac{d}{\mathrm{dx}} \left(x \sin y + y \cos x\right) = 0$

$x y ' \cos y + \sin y + y ' \cos x - y \sin x = 0$

$y ' \left(x \cos y + \cos x\right) = y \sin x - \sin y$

$y ' = \frac{y \sin x - \sin y}{x \cos y + \cos x}$