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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

3 π r^{2}

\frac{d}{d x} (x^{2} e^{- 0.04 x})

\frac{\partial}{\partial y} (x e^{- 2 x})

\frac{\partial}{\partial x} (x y^{2} z)

\int (3 - x)^{3} d x

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