What is the derivative of e^{2x}cos(4x) ?

The derivative of e^{2x}cos(4x) is 2e^{2x}cos(4x)-4e^{2x}sin(4x)

What is the first derivative of e^{2x}cos(4x) ?

The first derivative of e^{2x}cos(4x) is 2e^{2x}cos(4x)-4e^{2x}sin(4x)

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} cos (4 x))

2 e^{2 x} cos (4 x) - 4 e^{2 x} sin (4 x)

Solution steps

\frac{d}{d x} (e^{2 x} cos (4 x))

Apply the Product Rule:

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

f = e^{2 x}, g = cos (4 x)

= \frac{d}{d x} (e^{2 x}) cos (4 x) + \frac{d}{d x} (cos (4 x)) e^{2 x}

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

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= e^{2 x} \cdot 2 cos (4 x) + (- sin (4 x) \cdot 4) e^{2 x}

Simplify

= 2 e^{2 x} cos (4 x) - 4 e^{2 x} sin (4 x)

\int 4 x (2 x^{2} + 1)^{7} d x

\int 6 x^{4} - 5 x^{3} + 5 x^{2} + C d x

\frac{d y}{d x} = e^{2 y - x}

y = (7 x - 4) (2 + 6 x)

x \to \infty lim (arctan (1 - x))

What is the derivative of e^{2x}cos(4x) ?
The derivative of e^{2x}cos(4x) is 2e^{2x}cos(4x)-4e^{2x}sin(4x)
What is the first derivative of e^{2x}cos(4x) ?
The first derivative of e^{2x}cos(4x) is 2e^{2x}cos(4x)-4e^{2x}sin(4x)