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

The tangent of f(x)=(1+ln(x))/x ,\at x=e is y=-1/(e^2)x+3/e

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

tangent of

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

y = - \frac{1}{e ^{2}} x + \frac{3}{e}

Solution steps

Find the tangent point:

(e, \frac{2}{e})

Find the slope of

f (x) = \frac{1 + ln ( x )}{x} : \frac{df ( x )}{d x} = - \frac{ln ( 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 = - \frac{1}{e ^{2}}

Find the line with slope m=

- \frac{1}{e ^{2}}

and passing through

(e, \frac{2}{e}) : y = - \frac{1}{e ^{2}} x + \frac{3}{e}

y = - \frac{1}{e ^{2}} x + \frac{3}{e}

What is the tangent of f(x)=(1+ln(x))/x ,\at x=e ?
The tangent of f(x)=(1+ln(x))/x ,\at x=e is y=-1/(e^2)x+3/e