What is the derivative of 1-(1+x/(200)e^{-x/(200)}) ?

The derivative of 1-(1+x/(200)e^{-x/(200)}) is (e^{-x/(200)}x)/(40000)

What is the first derivative of 1-(1+x/(200)e^{-x/(200)}) ?

The first derivative of 1-(1+x/(200)e^{-x/(200)}) is (e^{-x/(200)}x)/(40000)

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\frac{d}{d x} (1 - (1 + \frac{x}{200}) e^{- \frac{x}{200}})

\frac{e ^{- \frac{x}{200}} x}{40000}

Solution steps

\frac{d}{d x} (1 - (1 + \frac{x}{200}) e^{- \frac{x}{200}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (1) - \frac{d}{d x} ((1 + \frac{x}{200}) e^{- \frac{x}{200}})

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

\frac{d}{d x} ((1 + \frac{x}{200}) e^{- \frac{x}{200}}) = - \frac{e ^{- \frac{x}{200}} x}{40000}

= 0 - (- \frac{e ^{- \frac{x}{200}} x}{40000})

Simplify

= \frac{e ^{- \frac{x}{200}} x}{40000}

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What is the derivative of 1-(1+x/(200)e^{-x/(200)}) ?
The derivative of 1-(1+x/(200)e^{-x/(200)}) is (e^{-x/(200)}x)/(40000)
What is the first derivative of 1-(1+x/(200)e^{-x/(200)}) ?
The first derivative of 1-(1+x/(200)e^{-x/(200)}) is (e^{-x/(200)}x)/(40000)