What is the derivative of e^{-2x}(1-x) ?

The derivative of e^{-2x}(1-x) is 2e^{-2x}x-3e^{-2x}

What is the first derivative of e^{-2x}(1-x) ?

The first derivative of e^{-2x}(1-x) is 2e^{-2x}x-3e^{-2x}

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\frac{d}{d x} (e^{- 2 x} (1 - x))

2 e^{- 2 x} x - 3 e^{- 2 x}

Solution steps

\frac{d}{d x} (e^{- 2 x} (1 - x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- 2 x}, g = 1 - x

= \frac{d}{d x} (e^{- 2 x}) (1 - x) + \frac{d}{d x} (1 - x) e^{- 2 x}

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

\frac{d}{d x} (1 - x) = - 1

= (- 2 e^{- 2 x}) (1 - x) + (- 1) e^{- 2 x}

Simplify

(- 2 e^{- 2 x}) (1 - x) + (- 1) e^{- 2 x} : 2 e^{- 2 x} x - 3 e^{- 2 x}

= 2 e^{- 2 x} x - 3 e^{- 2 x}

What is the derivative of e^{-2x}(1-x) ?
The derivative of e^{-2x}(1-x) is 2e^{-2x}x-3e^{-2x}
What is the first derivative of e^{-2x}(1-x) ?
The first derivative of e^{-2x}(1-x) is 2e^{-2x}x-3e^{-2x}