What is the d/(dt)(e^t(sin(t)+cos(t))) ?

The d/(dt)(e^t(sin(t)+cos(t))) is 2e^tcos(t)

What is the first d/(dt)(e^t(sin(t)+cos(t))) ?

The first d/(dt)(e^t(sin(t)+cos(t))) is 2e^tcos(t)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

2 e^{t} cos (t)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 2 e^{t} cos (t)

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