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Popular >

derivative of (3+2x)e^{-3x}

Solution

derivative of

(3 + 2 x) e^{- 3 x}

Solution

- 7 e^{- 3 x} - 6 e^{- 3 x} x

Solution steps

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

Apply the Product Rule:

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

f = 3 + 2 x, g = e^{- 3 x}

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

\frac{d}{d x} (3 + 2 x) = 2

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

= 2 e^{- 3 x} + (- 3 e^{- 3 x}) (3 + 2 x)

Simplify

2 e^{- 3 x} + (- 3 e^{- 3 x}) (3 + 2 x) : - 7 e^{- 3 x} - 6 e^{- 3 x} x

= - 7 e^{- 3 x} - 6 e^{- 3 x} x

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Frequently Asked Questions (FAQ)

What is the derivative of (3+2x)e^{-3x} ?
The derivative of (3+2x)e^{-3x} is -7e^{-3x}-6e^{-3x}x
What is the first derivative of (3+2x)e^{-3x} ?
The first derivative of (3+2x)e^{-3x} is -7e^{-3x}-6e^{-3x}x