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Popular >

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

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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