# How do you find an equation of the tangent line to the curve y=e^x/x at the point (1,e)?

Dec 13, 2016

Find the derivative and plug in our x-coordinate to find the slope of the tangent line. Then use that slope for a point-slope formula.

#### Explanation:

$y ' = \frac{{e}^{x} - x {e}^{x}}{x} ^ 2$

$y ' \left(1\right) = 0 = m$ This is our slope; a horizontal line.

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Since our slope($m$) is 0, our line will just be our y-coordinate: $e$

Therefore:

The equation of the tangent line is:

$y = e$