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Popular >

derivative of e^{-6x}cos(6x)

Solution

\frac{d}{d x} (e^{- 6 x} cos (6 x))

Solution

- 6 e^{- 6 x} cos (6 x) - 6 e^{- 6 x} sin (6 x)

Solution steps

\frac{d}{d x} (e^{- 6 x} cos (6 x))

Apply the Product Rule:

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

f = e^{- 6 x}, g = cos (6 x)

= \frac{d}{d x} (e^{- 6 x}) cos (6 x) + \frac{d}{d x} (cos (6 x)) e^{- 6 x}

\frac{d}{d x} (e^{- 6 x}) = - 6 e^{- 6 x}

\frac{d}{d x} (cos (6 x)) = - sin (6 x) \cdot 6

= (- 6 e^{- 6 x}) cos (6 x) + (- sin (6 x) \cdot 6) e^{- 6 x}

Simplify

= - 6 e^{- 6 x} cos (6 x) - 6 e^{- 6 x} sin (6 x)

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Frequently Asked Questions (FAQ)

What is the derivative of e^{-6x}cos(6x) ?
The derivative of e^{-6x}cos(6x) is -6e^{-6x}cos(6x)-6e^{-6x}sin(6x)
What is the first derivative of e^{-6x}cos(6x) ?
The first derivative of e^{-6x}cos(6x) is -6e^{-6x}cos(6x)-6e^{-6x}sin(6x)