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Popular Calculus >

derivative of 1000e^{-x/(10})

Solution

\frac{d}{d x} (1000 e^{- \frac{x}{10}})

Solution

- 100 e^{- \frac{x}{10}}

Solution steps

\frac{d}{d x} (1000 e^{- \frac{x}{10}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 1000 \frac{d}{d x} (e^{- \frac{x}{10}})

Apply the chain rule:

e^{- \frac{x}{10}} \frac{d}{d x} (- \frac{x}{10})

= e^{- \frac{x}{10}} \frac{d}{d x} (- \frac{x}{10})

\frac{d}{d x} (- \frac{x}{10}) = - \frac{1}{10}

= 1000 e^{- \frac{x}{10}} (- \frac{1}{10})

Simplify

1000 e^{- \frac{x}{10}} (- \frac{1}{10}) : - 100 e^{- \frac{x}{10}}

= - 100 e^{- \frac{x}{10}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 1000e^{-x/(10}) ?
The derivative of 1000e^{-x/(10}) is -100e^{-x/(10)}
What is the first derivative of 1000e^{-x/(10}) ?
The first derivative of 1000e^{-x/(10}) is -100e^{-x/(10)}