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

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

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

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

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

e^{- x} x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= e^{- x} x

\int \frac{2 x ^{5}}{1 - 6 x ^{6}} d x

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\frac{d}{d x} (- \frac{x}{8})

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