What is the tangent of e^{-2x} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of e^{-2x}

tangent of

e^{- 2 x}

y = - 2 e^{- 2 a_{0}} x + e^{- 2 a_{0}} + 2 a_{0} e^{- 2 a_{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, e^{- 2 a_{0}})

Find the slope of

y = e^{- 2 x} : \frac{d y}{d x} = - 2 e^{- 2 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 = - 2 e^{- 2 a_{0}}

Find the line with slope m=

- 2 e^{- 2 a_{0}}

and passing through

(a_{0}, e^{- 2 a_{0}}) : y = - 2 e^{- 2 a_{0}} x + e^{- 2 a_{0}} + 2 a_{0} e^{- 2 a_{0}}

y = - 2 e^{- 2 a_{0}} x + e^{- 2 a_{0}} + 2 a_{0} e^{- 2 a_{0}}

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