en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(dt)(e^{2t}cos(4t))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

derivative of f(x)=(x^4)sqrt(x^2+2)derivative of

f (x) = (x^{4}) x^{2} + 2

integral of (48x)/((x+1)^2(3x+1))

\int \frac{48 x}{( x + 1 ) ^{2} ( 3 x + 1 )} d x

t^2y^{''}-t(t+2)y^'+(t+2)y=0

t^{2} y^{^{''}} - t (t + 2) y^{^{'}} + (t + 2) y = 0

tangent of y=4x^2+3x(-3.27)tangent of

y = 4 x^{2} + 3 x (- 3.27)

limit as x approaches 2 of ((x+2))/(x-2)

x \to 2 lim (\frac{( x + 2 )}{x - 2})

Frequently Asked Questions (FAQ)

What is the d/(dt)(e^{2t}cos(4t)) ?
The d/(dt)(e^{2t}cos(4t)) is 2e^{2t}cos(4t)-4e^{2t}sin(4t)
What is the first d/(dt)(e^{2t}cos(4t)) ?
The first d/(dt)(e^{2t}cos(4t)) is 2e^{2t}cos(4t)-4e^{2t}sin(4t)