What is the derivative of f(x)=(x+2)^2e^{-x} ?

The derivative of f(x)=(x+2)^2e^{-x} is -e^{-x}x^2-2e^{-x}x

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

The first derivative of f(x)=(x+2)^2e^{-x} is -e^{-x}x^2-2e^{-x}x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = (x + 2)^{2} e^{- x}

- e^{- x} x^{2} - 2 e^{- x} x

Solution steps

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

Apply the Product Rule:

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

f = (x + 2)^{2}, g = e^{- x}

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

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

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

= 2 (x + 2) e^{- x} + (- e^{- x}) (x + 2)^{2}

Simplify

2 (x + 2) e^{- x} + (- e^{- x}) (x + 2)^{2} : - e^{- x} x^{2} - 2 e^{- x} x

= - e^{- x} x^{2} - 2 e^{- x} x

x \to - 1 lim (\frac{2 - 2}{x + 1})

sin (\frac{10 π}{x})

\frac{d}{d t} (- cot (t))

x \to 2 lim (\frac{2 x + 1}{5 - 3 x})

\int \frac{1}{( 1 - y ^{2} )} d y

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