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

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

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

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

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^{3 x} cos (2 x))

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int e (x) d x

\int \frac{x - 6}{x ^{2} + x - 6} d x

\frac{d}{d z} (ln ((cos (x) y)^{z}))

\int 8 x^{3} (2 x^{4} + 4) 4 d x

7 t \frac{d y}{d t} + y = t

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