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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int 1 + e^{2 x} d x

\frac{d}{d x} (ln ((x^{2} + 4 x + 5)^{3}))

\int e - e^{x} d x

\frac{1}{2} sin (4 t)

x y^{^{'}} + y = - 3 x

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