What is the d/(dt)(4e^tcos(t)) ?

The d/(dt)(4e^tcos(t)) is 4(e^tcos(t)-e^tsin(t))

What is the first d/(dt)(4e^tcos(t)) ?

The first d/(dt)(4e^tcos(t)) is 4(e^tcos(t)-e^tsin(t))

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\frac{d}{d t} (4 e^{t} cos (t))

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

Solution steps

\frac{d}{d t} (4 e^{t} cos (t))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \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)

= 4 (\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)

= 4 (e^{t} cos (t) + (- sin (t)) e^{t})

Simplify

= 4 (e^{t} cos (t) - e^{t} sin (t))

What is the d/(dt)(4e^tcos(t)) ?
The d/(dt)(4e^tcos(t)) is 4(e^tcos(t)-e^tsin(t))
What is the first d/(dt)(4e^tcos(t)) ?
The first d/(dt)(4e^tcos(t)) is 4(e^tcos(t)-e^tsin(t))