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Popular >

derivative of xe^{-3x}

Solution

\frac{d}{d x} (x e^{- 3 x})

Solution

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

Solution steps

\frac{d}{d x} (x e^{- 3 x})

Apply the Product Rule:

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

f = x, g = e^{- 3 x}

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

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

\frac{d}{d x} (e^{- 3 x}) = - 3 e^{- 3 x}

= 1 \cdot e^{- 3 x} + (- 3 e^{- 3 x}) x

Simplify

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

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x \to 0 lim (\frac{x - x}{x ^{2}})

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derivative of y=x(x^2+1)derivative of

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f (y) = cos^{2} (y)

Frequently Asked Questions (FAQ)

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