Find an equation of the tangent line to the curve at the given point.
y= e^x/x, (1,e).

I know that these are simpler than they look. I'm having difficulty keeping the formulas straight.

Question

Find an equation of the tangent line to the curve at the given point. 
y= e^x/x, (1,e).

I know that these are simpler than they look. I'm having difficulty keeping the formulas straight.

anonymous · Answer

So first differentiate the equation of the curve.

$$y = (e^x)/x$$
$$y' = (e^x)/x - (e^x)/x^2$$

anonymous · Answer

To solve for the slope, substitute 1 in place of x, since it is the x-coordinate of the given point.

$$m = (e^1)/1 - (e^1)/1^2$$
$$m = e-e$$
$$m = 0$$

anonymous · Answer

Use the point-slope formula to find the equation of the tangent line.
y - y1=m(x - x1)
y - e = 0(x - 1)
y = e

anonymous · Answer

Ugh, I knew it was simple! Thanks for the help! I feel silly now!

anonymous · Answer

np