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Popular >

derivative of e^{-0.5x}(4-x-2)

Solution

\frac{d}{d x} (e^{- 0.5 x} (4 - x) - 2)

Solution

0.5 e^{- 0.5 x} x - 3 e^{- 0.5 x}

Solution steps

\frac{d}{d x} (e^{- 0.5 x} (4 - x) - 2)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{- 0.5 x} (4 - x)) - \frac{d}{d x} (2)

\frac{d}{d x} (e^{- 0.5 x} (4 - x)) = 0.5 e^{- 0.5 x} x - 3 e^{- 0.5 x}

\frac{d}{d x} (2) = 0

= 0.5 e^{- 0.5 x} x - 3 e^{- 0.5 x} - 0

Simplify

= 0.5 e^{- 0.5 x} x - 3 e^{- 0.5 x}

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Frequently Asked Questions (FAQ)

What is the derivative of e^{-0.5x}(4-x-2) ?
The derivative of e^{-0.5x}(4-x-2) is 0.5e^{-0.5x}x-3e^{-0.5x}
What is the first derivative of e^{-0.5x}(4-x-2) ?
The first derivative of e^{-0.5x}(4-x-2) is 0.5e^{-0.5x}x-3e^{-0.5x}