en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(dt)(e^tsin(2t))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

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

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

integral of (4x^3-x^2+2)/(x^4-x^3+x^2)

\int \frac{4 x ^{3} - x ^{2} + 2}{x ^{4} - x ^{3} + x ^{2}} d x

4x^2(dy)/(dx)=(dy)/(dx)+4xe^{-y}

4 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 4 x e^{- y}

integral from 0 to 1 of pi(y-y^4)

\int_{0}^{1} π (y - y^{4}) d y

integral of (4x+6)/((x^2+3x+7)^3)

\int \frac{4 x + 6}{( x ^{2} + 3 x + 7 ) ^{3}} d x

Frequently Asked Questions (FAQ)

What is the d/(dt)(e^tsin(2t)) ?
The d/(dt)(e^tsin(2t)) is e^tsin(2t)+cos(2t)*2e^t
What is the first d/(dt)(e^tsin(2t)) ?
The first d/(dt)(e^tsin(2t)) is e^tsin(2t)+cos(2t)*2e^t