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Popular >

derivative of e^{-6x}-6e^{-6x}x

Solution

\frac{d}{d x} (e^{- 6 x} - 6 e^{- 6 x} x)

Solution

36 e^{- 6 x} x - 12 e^{- 6 x}

Solution steps

\frac{d}{d x} (e^{- 6 x} - 6 e^{- 6 x} x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{- 6 x}) - \frac{d}{d x} (6 e^{- 6 x} x)

\frac{d}{d x} (e^{- 6 x}) = - 6 e^{- 6 x}

\frac{d}{d x} (6 e^{- 6 x} x) = 6 (- 6 e^{- 6 x} x + e^{- 6 x})

= - 6 e^{- 6 x} - 6 (- 6 e^{- 6 x} x + e^{- 6 x})

Simplify

- 6 e^{- 6 x} - 6 (- 6 e^{- 6 x} x + e^{- 6 x}) : 36 e^{- 6 x} x - 12 e^{- 6 x}

= 36 e^{- 6 x} x - 12 e^{- 6 x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of e^{-6x}-6e^{-6x}x ?
The derivative of e^{-6x}-6e^{-6x}x is 36e^{-6x}x-12e^{-6x}
What is the first derivative of e^{-6x}-6e^{-6x}x ?
The first derivative of e^{-6x}-6e^{-6x}x is 36e^{-6x}x-12e^{-6x}