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

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Answer 1 · 2016-12-13T04:23:04

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.

#y'=(e^x-xe^x)/x^2#

#y'(1)=0=m# This is our slope; a horizontal line.

#y-y_1=m(x-x_1)#

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#