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Popular >

derivative of (2(axe^{-2x}+6))

Solution

\frac{d}{d x} ((2) (a x e^{- 2 x} + 6))

Solution

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

Solution steps

\frac{d}{d x} ((2) (a x e^{- 2 x} + 6))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (a x e^{- 2 x} + 6)

Apply the Sum/Difference Rule:

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

= 2 (\frac{d}{d x} (a x e^{- 2 x}) + \frac{d}{d x} (6))

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

\frac{d}{d x} (6) = 0

= 2 (a (e^{- 2 x} - 2 e^{- 2 x} x) + 0)

Simplify

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

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Frequently Asked Questions (FAQ)

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