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Popular >

derivative of e^{-x}cos(5x)

Solution

\frac{d}{d x} (e^{- x} cos (5 x))

Solution

- e^{- x} cos (5 x) - 5 e^{- x} sin (5 x)

Solution steps

\frac{d}{d x} (e^{- x} cos (5 x))

Apply the Product Rule:

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

f = e^{- x}, g = cos (5 x)

= \frac{d}{d x} (e^{- x}) cos (5 x) + \frac{d}{d x} (cos (5 x)) e^{- x}

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

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= (- e^{- x}) cos (5 x) + (- sin (5 x) \cdot 5) e^{- x}

Simplify

= - e^{- x} cos (5 x) - 5 e^{- x} sin (5 x)

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x \to 0 lim (\frac{( 3 e ^{- x} - 3 )}{x ^{2} - 2 x})

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

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x \to - 35 lim (34 + x)

(\partial)/(\partial y)(ye^y)

\frac{\partial}{\partial y} (y e^{y})

Frequently Asked Questions (FAQ)

What is the derivative of e^{-x}cos(5x) ?
The derivative of e^{-x}cos(5x) is -e^{-x}cos(5x)-5e^{-x}sin(5x)
What is the first derivative of e^{-x}cos(5x) ?
The first derivative of e^{-x}cos(5x) is -e^{-x}cos(5x)-5e^{-x}sin(5x)