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

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

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

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

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

- e^{- x} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot e^{- x} + (- e^{- x}) (1 + x) : - e^{- x} x

= - e^{- x} x

\int 8 x^{2} d x

4 y^{^{''}} - 5 y^{^{'}} = 0, y (- 2) = 0, y^{^{'}} (- 2) = 7

s + 1

\frac{d}{d x} (cos (x^{2} + 3))

\frac{d}{d x} (sin (e^{x^{5} s i n (x)}))

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