What is the derivative of 5x^2e^{-x} ?

The derivative of 5x^2e^{-x} is 5(2e^{-x}x-e^{-x}x^2)

What is the first derivative of 5x^2e^{-x} ?

The first derivative of 5x^2e^{-x} is 5(2e^{-x}x-e^{-x}x^2)

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

5 (2 e^{- x} x - e^{- x} x^{2})

Solution steps

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

Take the constant out:

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

= 5 \frac{d}{d x} (x^{2} e^{- x})

Apply the Product Rule:

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

f = x^{2}, g = e^{- x}

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

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

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

= 5 (2 x e^{- x} + (- e^{- x}) x^{2})

Simplify

= 5 (2 e^{- x} x - e^{- x} x^{2})

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What is the derivative of 5x^2e^{-x} ?
The derivative of 5x^2e^{-x} is 5(2e^{-x}x-e^{-x}x^2)
What is the first derivative of 5x^2e^{-x} ?
The first derivative of 5x^2e^{-x} is 5(2e^{-x}x-e^{-x}x^2)