# How do you find the derivative of  tan 2x = cos 3y?

Mar 16, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{2 {\sec}^{2} 2 x}{3 \sin 3 y}$

#### Explanation:

Differentiate both sides of the equation with respect to $x$:

$\frac{d}{\mathrm{dx}} \left(\tan 2 x\right) = \frac{d}{\mathrm{dx}} \left(\cos 3 y\right)$

using the chain rule:

$2 {\sec}^{2} 2 x = - 3 \frac{\mathrm{dy}}{\mathrm{dx}} \sin 3 y$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{2 {\sec}^{2} 2 x}{3 \sin 3 y}$