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Popular >

derivative of e^{-x}cos(3x)

Solution

\frac{d}{d x} (e^{- x} cos (3 x))

Solution

- e^{- x} cos (3 x) - 3 e^{- x} sin (3 x)

Solution steps

\frac{d}{d x} (e^{- x} cos (3 x))

Apply the Product Rule:

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

f = e^{- x}, g = cos (3 x)

= \frac{d}{d x} (e^{- x}) cos (3 x) + \frac{d}{d x} (cos (3 x)) e^{- x}

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

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= (- e^{- x}) cos (3 x) + (- sin (3 x) \cdot 3) e^{- x}

Simplify

= - e^{- x} cos (3 x) - 3 e^{- x} sin (3 x)

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\int_{1}^{3} t ln (t) d t

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\frac{d}{d x} (ln (x^{3}) + e^{2 x})

Frequently Asked Questions (FAQ)

What is the derivative of e^{-x}cos(3x) ?
The derivative of e^{-x}cos(3x) is -e^{-x}cos(3x)-3e^{-x}sin(3x)
What is the first derivative of e^{-x}cos(3x) ?
The first derivative of e^{-x}cos(3x) is -e^{-x}cos(3x)-3e^{-x}sin(3x)