What is the tangent of x/(e^x) ?

The tangent of x/(e^x) is y=(1-a_{0})/(e^{a_{0)}}x+(a_{0}^2)/(e^{a_{0)}}

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tangent of x/(e^x)

tangent of

\frac{x}{e ^{x}}

y = \frac{1 - a _{0}}{e ^{a_{0}}} x + \frac{a _{0}^{2}}{e ^{a_{0}}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{a _{0}}{e ^{a_{0}}})

Find the slope of

y = \frac{x}{e ^{x}} : \frac{d y}{d x} = \frac{1 - x}{e ^{x}}

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 - a _{0}}{e ^{a_{0}}}

Find the line with slope m=

\frac{1 - a _{0}}{e ^{a_{0}}}

and passing through

(a_{0}, \frac{a _{0}}{e ^{a_{0}}}) : y = \frac{1 - a _{0}}{e ^{a_{0}}} x + \frac{a _{0}^{2}}{e ^{a_{0}}}

y = \frac{1 - a _{0}}{e ^{a_{0}}} x + \frac{a _{0}^{2}}{e ^{a_{0}}}

n = 0 \sum \infty (- 1)^{n + 1}

- 7

y = t e^{- t}

x y^{2} \frac{d y}{d x} = y^{3} - x^{3}, y (1) = 3

\int \frac{x}{2 x - 1} d x

What is the tangent of x/(e^x) ?
The tangent of x/(e^x) is y=(1-a_{0})/(e^{a_{0)}}x+(a_{0}^2)/(e^{a_{0)}}