What is the tangent of f(x)=(e^x)/x ,\at x=1 ?

The tangent of f(x)=(e^x)/x ,\at x=1 is y=e

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tangent of f(x)=(e^x)/x ,\at x=1

tangent of

f (x) = \frac{e ^{x}}{x}, at x = 1

y = e

Solution steps

Find the tangent point:

(1, e)

Find the slope of

f (x) = \frac{e ^{x}}{x} : \frac{df ( x )}{d x} = \frac{e ^{x} x - e ^{x}}{x ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 0

Find the line with slope m=

0

and passing through

(1, e) : y = e

y = e

\frac{d}{d x} (\frac{3 x + 2}{5 - 4 x})

\frac{\partial}{\partial x} (\frac{1}{ln ( \frac{y}{x} )})

s im pl i f y ln (\frac{( x + 6 ) ^{4} e ^{5 x^{3} - 3}}{x + 2 x ^{3}})

d er i v a t i v e ln (y^{2})

s im pl i f y \frac{7}{4} x^{4} - \frac{6}{5} x^{3}

What is the tangent of f(x)=(e^x)/x ,\at x=1 ?
The tangent of f(x)=(e^x)/x ,\at x=1 is y=e