en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

d/(dt)(e^{3t}cos(2t))

Solution

\frac{d}{d t} (e^{3 t} cos (2 t))

Solution

3 e^{3 t} cos (2 t) - 2 e^{3 t} sin (2 t)

Solution steps

\frac{d}{d t} (e^{3 t} cos (2 t))

Apply the Product Rule:

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

f = e^{3 t}, g = cos (2 t)

= \frac{d}{d t} (e^{3 t}) cos (2 t) + \frac{d}{d t} (cos (2 t)) e^{3 t}

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

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

= e^{3 t} \cdot 3 cos (2 t) + (- sin (2 t) \cdot 2) e^{3 t}

Simplify

= 3 e^{3 t} cos (2 t) - 2 e^{3 t} sin (2 t)

Graph

Popular Examples

slope of y=x^2+5x

s l o p e y = x^{2} + 5 x

integral of (sin(x))/(sqrt(4-cos(x)))

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

integral of 4x-4x^2

\int 4 x - 4 x^{2} d x

derivative of arcsin(3x^4)

\frac{d}{d x} (arcsin (3 x^{4}))

(dy)/(dx)=(6y^3)/((3-2x)^2),y(0)=-1

\frac{d y}{d x} = \frac{6 y ^{3}}{( 3 - 2 x ) ^{2}}, y (0) = - 1

Frequently Asked Questions (FAQ)

What is the d/(dt)(e^{3t}cos(2t)) ?
The d/(dt)(e^{3t}cos(2t)) is 3e^{3t}cos(2t)-2e^{3t}sin(2t)
What is the first d/(dt)(e^{3t}cos(2t)) ?
The first d/(dt)(e^{3t}cos(2t)) is 3e^{3t}cos(2t)-2e^{3t}sin(2t)