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Popular Calculus >

derivative of y=e^{-x}cos(2x)

Solution

derivative of

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

Solution

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

Solution steps

\frac{d}{d x} (e^{- x} cos (2 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- x}, g = cos (2 x)

= \frac{d}{d x} (e^{- x}) cos (2 x) + \frac{d}{d x} (cos (2 x)) e^{- x}

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= (- e^{- x}) cos (2 x) + (- sin (2 x) \cdot 2) e^{- x}

Simplify

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

Graph

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Frequently Asked Questions (FAQ)

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