What is the derivative of 4x^4e^{-x} ?

The derivative of 4x^4e^{-x} is 4(4e^{-x}x^3-e^{-x}x^4)

What is the first derivative of 4x^4e^{-x} ?

The first derivative of 4x^4e^{-x} is 4(4e^{-x}x^3-e^{-x}x^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (4 x^{4} e^{- x})

4 (4 e^{- x} x^{3} - e^{- x} x^{4})

Solution steps

\frac{d}{d x} (4 x^{4} e^{- x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x^{4} e^{- x})

Apply the Product Rule:

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

f = x^{4}, g = e^{- x}

= 4 (\frac{d}{d x} (x^{4}) e^{- x} + \frac{d}{d x} (e^{- x}) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 (4 x^{3} e^{- x} + (- e^{- x}) x^{4})

Simplify

= 4 (4 e^{- x} x^{3} - e^{- x} x^{4})

\int \frac{y - 1}{y + 1} d y

\frac{d}{d x} (3 x ln (4 x) - 3 x)

\frac{\partial}{\partial x} (6 ze x yz)

t y^{^{'}} + 3 y = t^{2}

What is the derivative of 4x^4e^{-x} ?
The derivative of 4x^4e^{-x} is 4(4e^{-x}x^3-e^{-x}x^4)
What is the first derivative of 4x^4e^{-x} ?
The first derivative of 4x^4e^{-x} is 4(4e^{-x}x^3-e^{-x}x^4)