en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

derivative of f(x)=ln(4-x^8)derivative of

f (x) = ln (4 - x^{8})

(d^2y)/(dx^2)-49(dy)/(dx)=e^{7x}

\frac{d ^{2} y}{d x ^{2}} - 49 \frac{d y}{d x} = e^{7 x}

integral from 0 to 1 of xcos(2pix)

\int_{0}^{1} x cos (2 π x) d x

derivative of-2x+5 derivative of

- 2 x + 5

integral of xsec^2(6x)

\int x sec^{2} (6 x) d x

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)