# How do you use implicit differentiation to isolate dy/dx in this equation?

## 4sin(x-y)=4ysinx

Nov 2, 2016

$\frac{4 \cos \left(x - y\right) - 4 y \cos x}{4 \sin x + 4 \cos \left(x - y\right)} = \frac{\mathrm{dy}}{\mathrm{dx}}$

#### Explanation:

$4 \sin \left(x - y\right) = 4 y \sin x$

$4 \cos \left(x - y\right) - 4 \cos \left(x - y\right) \frac{\mathrm{dy}}{\mathrm{dx}} = 4 y \cos x + 4 \sin x \frac{\mathrm{dy}}{\mathrm{dx}}$

$4 \cos \left(x - y\right) - 4 y \cos x = 4 \sin x \frac{\mathrm{dy}}{\mathrm{dx}} + 4 \cos \left(x - y\right) \frac{\mathrm{dy}}{\mathrm{dx}}$

$4 \cos \left(x - y\right) - 4 y \cos x = \left(4 \sin x + 4 \cos \left(x - y\right)\right) \frac{\mathrm{dy}}{\mathrm{dx}}$

$\frac{4 \cos \left(x - y\right) - 4 y \cos x}{4 \sin x + 4 \cos \left(x - y\right)} = \frac{\mathrm{dy}}{\mathrm{dx}}$