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

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

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

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

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

e^{- x} x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (1) = 0

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

= 0 - (- e^{- x} x)

Simplify

= e^{- x} x

\int \frac{1}{( 2 + x ) 1 + x} d x

f (x) = x^{4} - 2 x^{2} + 1, at x = 2

\int_{0}^{π} sin (x) sin (3 x) d x

\frac{x ^{2}}{x ^{2} + 3}

y^{^{'}} = x^{2} y - y + x^{2} - 1

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