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Popular >

derivative of (5+4x)e^{-5x}

Solution

derivative of

(5 + 4 x) e^{- 5 x}

Solution

- 21 e^{- 5 x} - 20 e^{- 5 x} x

Solution steps

\frac{d}{d x} ((5 + 4 x) e^{- 5 x})

Apply the Product Rule:

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

f = 5 + 4 x, g = e^{- 5 x}

= \frac{d}{d x} (5 + 4 x) e^{- 5 x} + \frac{d}{d x} (e^{- 5 x}) (5 + 4 x)

\frac{d}{d x} (5 + 4 x) = 4

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

= 4 e^{- 5 x} + (- 5 e^{- 5 x}) (5 + 4 x)

Simplify

4 e^{- 5 x} + (- 5 e^{- 5 x}) (5 + 4 x) : - 21 e^{- 5 x} - 20 e^{- 5 x} x

= - 21 e^{- 5 x} - 20 e^{- 5 x} x

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Frequently Asked Questions (FAQ)

What is the derivative of (5+4x)e^{-5x} ?
The derivative of (5+4x)e^{-5x} is -21e^{-5x}-20e^{-5x}x
What is the first derivative of (5+4x)e^{-5x} ?
The first derivative of (5+4x)e^{-5x} is -21e^{-5x}-20e^{-5x}x