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Popular >

derivative of e^{-5x}-5e^{-5x}x

Solution

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

Solution

25 e^{- 5 x} x - 10 e^{- 5 x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

- 5 e^{- 5 x} - 5 (- 5 e^{- 5 x} x + e^{- 5 x}) : 25 e^{- 5 x} x - 10 e^{- 5 x}

= 25 e^{- 5 x} x - 10 e^{- 5 x}

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Frequently Asked Questions (FAQ)

What is the derivative of e^{-5x}-5e^{-5x}x ?
The derivative of e^{-5x}-5e^{-5x}x is 25e^{-5x}x-10e^{-5x}
What is the first derivative of e^{-5x}-5e^{-5x}x ?
The first derivative of e^{-5x}-5e^{-5x}x is 25e^{-5x}x-10e^{-5x}