en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^{3x}cos(6x)

Solution

derivative of

e^{3 x} cos (6 x)

Solution

3 e^{3 x} cos (6 x) - 6 e^{3 x} sin (6 x)

Solution steps

\frac{d}{d x} (e^{3 x} cos (6 x))

Apply the Product Rule:

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

f = e^{3 x}, g = cos (6 x)

= \frac{d}{d x} (e^{3 x}) cos (6 x) + \frac{d}{d x} (cos (6 x)) e^{3 x}

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

\frac{d}{d x} (cos (6 x)) = - sin (6 x) \cdot 6

= e^{3 x} \cdot 3 cos (6 x) + (- sin (6 x) \cdot 6) e^{3 x}

Simplify

= 3 e^{3 x} cos (6 x) - 6 e^{3 x} sin (6 x)

Popular Examples

5 x y^{^{'}} - 2 y = 9 x^{2}

derivative of (x^3/3-(x^2)/2-6x)

\frac{d}{d x} (\frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x)

derivative of e^xx^5+10e^xx^4+20e^xx^3

\frac{d}{d x} (e^{x} x^{5} + 10 e^{x} x^{4} + 20 e^{x} x^{3})

integral of 9sin^2(x)cos(x)

\int 9 sin^{2} (x) cos (x) d x

f (x) = 4 x + 5

Frequently Asked Questions (FAQ)

What is the derivative of e^{3x}cos(6x) ?
The derivative of e^{3x}cos(6x) is 3e^{3x}cos(6x)-6e^{3x}sin(6x)
What is the first derivative of e^{3x}cos(6x) ?
The first derivative of e^{3x}cos(6x) is 3e^{3x}cos(6x)-6e^{3x}sin(6x)