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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of e^{-x}

tangent of

e^{- x}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = e^{- x}

x = a_{0} : m = - e^{- a_{0}}

Find the line with slope m=

- e^{- a_{0}}

and passing through

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

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

y^{^{'}} = 2 x + 4 y

\int \frac{x}{2 + 3 x} d x

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

\int_{- 1}^{0} 2 x - e^{x} d x

\frac{t}{4}

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