What is the derivative of e^{-2x}sin(3x) ?

The derivative of e^{-2x}sin(3x) is -2e^{-2x}sin(3x)+3e^{-2x}cos(3x)

What is the first derivative of e^{-2x}sin(3x) ?

The first derivative of e^{-2x}sin(3x) is -2e^{-2x}sin(3x)+3e^{-2x}cos(3x)

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\frac{d}{d x} (e^{- 2 x} sin (3 x))

- 2 e^{- 2 x} sin (3 x) + 3 e^{- 2 x} cos (3 x)

Solution steps

\frac{d}{d x} (e^{- 2 x} sin (3 x))

Apply the Product Rule:

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

f = e^{- 2 x}, g = sin (3 x)

= \frac{d}{d x} (e^{- 2 x}) sin (3 x) + \frac{d}{d x} (sin (3 x)) e^{- 2 x}

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

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

= (- 2 e^{- 2 x}) sin (3 x) + cos (3 x) \cdot 3 e^{- 2 x}

Simplify

= - 2 e^{- 2 x} sin (3 x) + 3 e^{- 2 x} cos (3 x)

x \to - 1 lim (2 x^{2} - 5 x + 1)

x^{\frac{7}{3}}

\frac{d}{d x} (- x + 6)

- \frac{1}{2} y = \frac{d y}{d t}

\frac{2 s - 6}{s ^{2} + 9}

What is the derivative of e^{-2x}sin(3x) ?
The derivative of e^{-2x}sin(3x) is -2e^{-2x}sin(3x)+3e^{-2x}cos(3x)
What is the first derivative of e^{-2x}sin(3x) ?
The first derivative of e^{-2x}sin(3x) is -2e^{-2x}sin(3x)+3e^{-2x}cos(3x)