en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of e^{2x}cos(4x)

Solution

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

Solution

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)

Graph

Popular Examples

integral of 6x^4-5x^3+5x^2+C

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

limit as x approaches infinity of arctan(1-x)

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

limit as x approaches 0+of arctan(ln(x))

x \to 0 + lim (arctan (ln (x)))

(dv)/(dx)-1/x v=8

\frac{d v}{d x} - \frac{1}{x} v = 8

derivative of (ln(x))/(e^x)

d er i v a t i v e \frac{ln ( x )}{e ^{x}}

Frequently Asked Questions (FAQ)

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)