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Popular Calculus >

derivative of (7+2xe^{-3x})

Solution

\frac{d}{d x} ((7 + 2 x) e^{- 3 x})

Solution

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

Solution steps

\frac{d}{d x} ((7 + 2 x) e^{- 3 x})

Apply the Product Rule:

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

f = 7 + 2 x, g = e^{- 3 x}

= \frac{d}{d x} (7 + 2 x) e^{- 3 x} + \frac{d}{d x} (e^{- 3 x}) (7 + 2 x)

\frac{d}{d x} (7 + 2 x) = 2

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

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

Simplify

2 e^{- 3 x} + (- 3 e^{- 3 x}) (7 + 2 x) : - 19 e^{- 3 x} - 6 e^{- 3 x} x

= - 19 e^{- 3 x} - 6 e^{- 3 x} x

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (7+2xe^{-3x}) ?
The derivative of (7+2xe^{-3x}) is -19e^{-3x}-6e^{-3x}x
What is the first derivative of (7+2xe^{-3x}) ?
The first derivative of (7+2xe^{-3x}) is -19e^{-3x}-6e^{-3x}x