What is the derivative of 2e^{-1.5x}cos(3x) ?

The derivative of 2e^{-1.5x}cos(3x) is 2(-1.5e^{-1.5x}cos(3x)-3e^{-1.5x}sin(3x))

What is the first derivative of 2e^{-1.5x}cos(3x) ?

The first derivative of 2e^{-1.5x}cos(3x) is 2(-1.5e^{-1.5x}cos(3x)-3e^{-1.5x}sin(3x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (2 e^{- 1.5 x} cos (3 x))

2 (- 1.5 e^{- 1.5 x} cos (3 x) - 3 e^{- 1.5 x} sin (3 x))

Solution steps

\frac{d}{d x} (2 e^{- 1.5 x} cos (3 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (e^{- 1.5 x} cos (3 x))

Apply the Product Rule:

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

f = e^{- 1.5 x}, g = cos (3 x)

= 2 (\frac{d}{d x} (e^{- 1.5 x}) cos (3 x) + \frac{d}{d x} (cos (3 x)) e^{- 1.5 x})

\frac{d}{d x} (e^{- 1.5 x}) = - 1.5 e^{- 1.5 x}

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

= 2 ((- 1.5 e^{- 1.5 x}) cos (3 x) + (- sin (3 x) \cdot 3) e^{- 1.5 x})

Simplify

= 2 (- 1.5 e^{- 1.5 x} cos (3 x) - 3 e^{- 1.5 x} sin (3 x))

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

(2, 5), (8, 12)

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

\int \frac{4 - 9 x ^{2}}{x} d x

x \to 0 - lim (\frac{x ^{2}}{2} - \frac{8}{x})

What is the derivative of 2e^{-1.5x}cos(3x) ?
The derivative of 2e^{-1.5x}cos(3x) is 2(-1.5e^{-1.5x}cos(3x)-3e^{-1.5x}sin(3x))
What is the first derivative of 2e^{-1.5x}cos(3x) ?
The first derivative of 2e^{-1.5x}cos(3x) is 2(-1.5e^{-1.5x}cos(3x)-3e^{-1.5x}sin(3x))