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

The d/(dt)(e^t*cos(t)) is e^tcos(t)-e^tsin(t)

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

The first d/(dt)(e^t*cos(t)) is e^tcos(t)-e^tsin(t)

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

(\frac{1}{2}, 2), (6, 2)

\int_{- 3}^{0} \frac{1}{9 + 2 x} d x

x \to 2 lim (\frac{5 x - 1}{x - 2})

\int x e^{x} - x d x

\int arcsin (x + 2) d x

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