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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

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

Simplify

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

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