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

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

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

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

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derivative of

x e^{- 5 x}

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{- 5 x} + (- 5 e^{- 5 x}) x

Simplify

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

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