# What is the slope of the tangent line of (y/x)e^(y/x)= C , where C is an arbitrary constant, at (-3,1)?

##### 1 Answer
Jan 26, 2017

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{1}{3}$

#### Explanation:

Putting $y = \lambda x$ we have

$\lambda {e}^{\lambda} = C$

Making $\setminus \lambda = - \frac{1}{3}$ we are imposing also $\frac{\mathrm{dy}}{\mathrm{dy}} = \lambda = - \frac{1}{3}$