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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{- 2}, g = e^{x}

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

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

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

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

Simplify

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

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

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