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Popular >

derivative of-e^{-x}sin(x+e^{-x}cos(x))

Solution

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

Solution

- 2 e^{- x} cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= - (- e^{- x} sin (x) + e^{- x} cos (x)) - e^{- x} cos (x) - e^{- x} sin (x)

Simplify

= - 2 e^{- x} cos (x)

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\int_{- 8}^{8} \frac{( 64 - x ^{2} )}{2} d x

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derivative of f(x)=e^{2x+1}derivative of

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Frequently Asked Questions (FAQ)

What is the derivative of-e^{-x}sin(x+e^{-x}cos(x)) ?
The derivative of-e^{-x}sin(x+e^{-x}cos(x)) is -2e^{-x}cos(x)
What is the first derivative of-e^{-x}sin(x+e^{-x}cos(x)) ?
The first derivative of-e^{-x}sin(x+e^{-x}cos(x)) is -2e^{-x}cos(x)