What is the derivative of (e^{-x}/(x^2)) ?

The derivative of (e^{-x}/(x^2)) is -(e^{-x}(x+2))/(x^3)

What is the first derivative of (e^{-x}/(x^2)) ?

The first derivative of (e^{-x}/(x^2)) is -(e^{-x}(x+2))/(x^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{e ^{- x}}{x ^{2}})

- \frac{e ^{- x} ( x + 2 )}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{e ^{- x}}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{- x} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) e ^{- x}}{( x ^{2} ) ^{2}}

\frac{d}{d x} (e^{- x}) = - e^{- x}

\frac{d}{d x} (x^{2}) = 2 x

= \frac{( - e ^{- x} ) x ^{2} - 2 x e ^{- x}}{( x ^{2} ) ^{2}}

Simplify

\frac{( - e ^{- x} ) x ^{2} - 2 x e ^{- x}}{( x ^{2} ) ^{2}} : - \frac{e ^{- x} ( x + 2 )}{x ^{3}}

= - \frac{e ^{- x} ( x + 2 )}{x ^{3}}

What is the derivative of (e^{-x}/(x^2)) ?
The derivative of (e^{-x}/(x^2)) is -(e^{-x}(x+2))/(x^3)
What is the first derivative of (e^{-x}/(x^2)) ?
The first derivative of (e^{-x}/(x^2)) is -(e^{-x}(x+2))/(x^3)