What is the tangent of f(x)=(2ln(x))/x ,\at x=e ?

The tangent of f(x)=(2ln(x))/x ,\at x=e is y= 2/e

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tangent of f(x)=(2ln(x))/x ,\at x=e

tangent of

f (x) = \frac{2 ln ( x )}{x}, at x = e

y = \frac{2}{e}

Solution steps

Find the tangent point:

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

Find the slope of

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

Compute the slope of

f (x) = \frac{2 ln ( x )}{x}

x = e : m = 0

Find the line with slope m=

0

and passing through

(e, \frac{2}{e}) : y = \frac{2}{e}

y = \frac{2}{e}

\int \frac{- x}{x ^{2} + y ^{2}} d y

\int e^{- 2 x} \cdot x d x

cos (2 x + \frac{3 π}{2})

\int \frac{1}{( 196 + x ^{2} ) ^{\frac{3}{2}}} d x

x \to - 1 lim (g (x))

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