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

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

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

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

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

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

Solution steps

\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}

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

Simplify

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

\frac{d}{d x} ((csc (x) + cot (x))^{- 1})

n = 0 \sum \infty - \frac{n}{2}

x^{4} + 6 x^{2} - x

4 x y^{^{'}} - 20 y = x^{- 5}

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

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