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

The derivative of e^{-3x}sin(sqrt(3)x) is -3e^{-3x}sin(sqrt(3)x)+sqrt(3)e^{-3x}cos(sqrt(3)x)

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

The first derivative of e^{-3x}sin(sqrt(3)x) is -3e^{-3x}sin(sqrt(3)x)+sqrt(3)e^{-3x}cos(sqrt(3)x)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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