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Popular >

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

Solution

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

Solution

- \frac{1}{10} e^{- \frac{x}{10}} + sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

Simplify

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

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Frequently Asked Questions (FAQ)

What is the derivative of e^{-x/(10}-cos(x)) ?
The derivative of e^{-x/(10}-cos(x)) is -1/10 e^{-x/(10)}+sin(x)
What is the first derivative of e^{-x/(10}-cos(x)) ?
The first derivative of e^{-x/(10}-cos(x)) is -1/10 e^{-x/(10)}+sin(x)