# How do you implicitly differentiate 2=e^(xy)cosy ?

Jun 7, 2016

$\frac{y}{\tan y - x}$

#### Explanation:

You could differentiate right away, but to make things simpler let us take the natural logarithm on both sides:

$\ln 2 = x y + \ln \left(\cos y\right)$

Differentiating with respect to $x$ on both sides:

0 = y + x dy/dx + 1/(cos y) * (–sin y) * dy/dx
$0 = y + x \frac{\mathrm{dy}}{\mathrm{dx}} - \tan y \cdot \frac{\mathrm{dy}}{\mathrm{dx}}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{y}{\tan y - x}$