What is the derivative of x^6e^{-x} ?

The derivative of x^6e^{-x} is 6e^{-x}x^5-e^{-x}x^6

What is the first derivative of x^6e^{-x} ?

The first derivative of x^6e^{-x} is 6e^{-x}x^5-e^{-x}x^6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (x^{6} e^{- x})

6 e^{- x} x^{5} - e^{- x} x^{6}

Solution steps

\frac{d}{d x} (x^{6} e^{- x})

Apply the Product Rule:

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

f = x^{6}, g = e^{- x}

= \frac{d}{d x} (x^{6}) e^{- x} + \frac{d}{d x} (e^{- x}) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 6 x^{5} e^{- x} + (- e^{- x}) x^{6}

Simplify

= 6 e^{- x} x^{5} - e^{- x} x^{6}

ln (x), 6

\frac{d}{d x} (8 + 3 sin (x))

\int_{0}^{1} x^{\frac{1}{2}} d x

n = 1 \sum \infty \frac{1}{2 ^{n} n !}

x y^{^{'}} + y = 37 x

What is the derivative of x^6e^{-x} ?
The derivative of x^6e^{-x} is 6e^{-x}x^5-e^{-x}x^6
What is the first derivative of x^6e^{-x} ?
The first derivative of x^6e^{-x} is 6e^{-x}x^5-e^{-x}x^6