en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^t*cos(2t)

Solution

derivative of

e^{t} \cdot cos (2 t)

Solution

e^{t} cos (2 t) - 2 e^{t} sin (2 t)

Solution steps

\frac{d}{d t} (e^{t} cos (2 t))

Apply the Product Rule:

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

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

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

\frac{d}{d t} (e^{t}) = e^{t}

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

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

Simplify

= e^{t} cos (2 t) - 2 e^{t} sin (2 t)

Popular Examples

integral from 0 to 2 of t^3(3+t^4)^3

\int_{0}^{2} t^{3} (3 + t^{4})^{3} d t

integral of ((2x)/(1+x^2))

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

derivative of f(x)=sqrt(2)-sqrt(x)derivative of

f (x) = 2 - x

integral of ((x+1))/(x^2(x-1))

\int \frac{( x + 1 )}{x ^{2} ( x - 1 )} d x

integral from 300 to 360 of (2400)/(x^2)

\int_{300}^{360} \frac{2400}{x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of e^t*cos(2t) ?
The derivative of e^t*cos(2t) is e^tcos(2t)-2e^tsin(2t)
What is the first derivative of e^t*cos(2t) ?
The first derivative of e^t*cos(2t) is e^tcos(2t)-2e^tsin(2t)