What is the derivative of e^tcos(t) ?

The derivative of e^tcos(t) is e^tcos(t)-e^tsin(t)

What is the first derivative of e^tcos(t) ?

The first derivative of e^tcos(t) is e^tcos(t)-e^tsin(t)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

e^{t} cos (t)

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

(x - 6) y^{^{'}} + y = x^{2} - 20

\int x^{3} 16 - x^{2} d x

\int 8 x - 10 y + 2 d y

\int (ln (x) cos (x)) sin (x) d x

y^{^{'}} = \frac{( 1 - 2 t )}{y}

What is the derivative of e^tcos(t) ?
The derivative of e^tcos(t) is e^tcos(t)-e^tsin(t)
What is the first derivative of e^tcos(t) ?
The first derivative of e^tcos(t) is e^tcos(t)-e^tsin(t)