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Popular Calculus >

derivative of-8e^{-x/(10}-40)

Solution

\frac{d}{d x} (- 8 e^{- \frac{x}{10}} - 40)

Solution

\frac{4}{5} e^{- \frac{x}{10}}

Solution steps

\frac{d}{d x} (- 8 e^{- \frac{x}{10}} - 40)

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (8 e^{- \frac{x}{10}}) - \frac{d}{d x} (40)

\frac{d}{d x} (8 e^{- \frac{x}{10}}) = - \frac{4}{5} e^{- \frac{x}{10}}

\frac{d}{d x} (40) = 0

= - (- \frac{4}{5} e^{- \frac{x}{10}}) - 0

Simplify

= \frac{4}{5} e^{- \frac{x}{10}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of-8e^{-x/(10}-40) ?
The derivative of-8e^{-x/(10}-40) is 4/5 e^{-x/(10)}
What is the first derivative of-8e^{-x/(10}-40) ?
The first derivative of-8e^{-x/(10}-40) is 4/5 e^{-x/(10)}