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Popular >

derivative of Axe^{-3x}

Solution

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

Solution

A (e^{- 3 x} - 3 e^{- 3 x} x)

Solution steps

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

Take the constant out:

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

= A \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}

= A (\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}

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

Simplify

= A (e^{- 3 x} - 3 e^{- 3 x} x)

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Frequently Asked Questions (FAQ)

What is the derivative of Axe^{-3x} ?
The derivative of Axe^{-3x} is A(e^{-3x}-3e^{-3x}x)
What is the first derivative of Axe^{-3x} ?
The first derivative of Axe^{-3x} is A(e^{-3x}-3e^{-3x}x)