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

The derivative of x^5e^{-x} is 5e^{-x}x^4-e^{-x}x^5

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

The first derivative of x^5e^{-x} is 5e^{-x}x^4-e^{-x}x^5

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\frac{d}{d x} (x^{5} e^{- x})

5 e^{- x} x^{4} - e^{- x} x^{5}

Solution steps

\frac{d}{d x} (x^{5} e^{- x})

Apply the Product Rule:

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

f = x^{5}, g = e^{- x}

= \frac{d}{d x} (x^{5}) e^{- x} + \frac{d}{d x} (e^{- x}) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} e^{- x} + (- e^{- x}) x^{5}

Simplify

= 5 e^{- x} x^{4} - e^{- x} x^{5}

\frac{d}{d x} (\frac{3 x + 5}{x ^{2} - x})

\int \frac{5}{x ln ( 6 x )} d x

\int_{0}^{3} x 16 - x^{2} d x

\int \frac{1}{x ^{2} x ^{2} - 3} d x

x \to 0 lim (- x ln (x) - x)

What is the derivative of x^5e^{-x} ?
The derivative of x^5e^{-x} is 5e^{-x}x^4-e^{-x}x^5
What is the first derivative of x^5e^{-x} ?
The first derivative of x^5e^{-x} is 5e^{-x}x^4-e^{-x}x^5