What is the derivative of e^{-8x}sin(8x) ?

The derivative of e^{-8x}sin(8x) is -8e^{-8x}sin(8x)+8e^{-8x}cos(8x)

What is the first derivative of e^{-8x}sin(8x) ?

The first derivative of e^{-8x}sin(8x) is -8e^{-8x}sin(8x)+8e^{-8x}cos(8x)

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\frac{d}{d x} (e^{- 8 x} sin (8 x))

- 8 e^{- 8 x} sin (8 x) + 8 e^{- 8 x} cos (8 x)

Solution steps

\frac{d}{d x} (e^{- 8 x} sin (8 x))

Apply the Product Rule:

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

f = e^{- 8 x}, g = sin (8 x)

= \frac{d}{d x} (e^{- 8 x}) sin (8 x) + \frac{d}{d x} (sin (8 x)) e^{- 8 x}

\frac{d}{d x} (e^{- 8 x}) = - 8 e^{- 8 x}

\frac{d}{d x} (sin (8 x)) = cos (8 x) \cdot 8

= (- 8 e^{- 8 x}) sin (8 x) + cos (8 x) \cdot 8 e^{- 8 x}

Simplify

= - 8 e^{- 8 x} sin (8 x) + 8 e^{- 8 x} cos (8 x)

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\frac{d}{d x} (\frac{1 - x}{e ^{2 x}})

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What is the derivative of e^{-8x}sin(8x) ?
The derivative of e^{-8x}sin(8x) is -8e^{-8x}sin(8x)+8e^{-8x}cos(8x)
What is the first derivative of e^{-8x}sin(8x) ?
The first derivative of e^{-8x}sin(8x) is -8e^{-8x}sin(8x)+8e^{-8x}cos(8x)