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Popular >

d/(dt)(5e^tcos(t))

Solution

\frac{d}{d t} (5 e^{t} cos (t))

Solution

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

Solution steps

\frac{d}{d t} (5 e^{t} cos (t))

Take the constant out:

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

= 5 \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)

= 5 (\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)

= 5 (e^{t} cos (t) + (- sin (t)) e^{t})

Simplify

= 5 (e^{t} cos (t) - e^{t} sin (t))

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\int (θ^{6} + sec^{2} (θ)) d θ

Frequently Asked Questions (FAQ)

What is the d/(dt)(5e^tcos(t)) ?
The d/(dt)(5e^tcos(t)) is 5(e^tcos(t)-e^tsin(t))
What is the first d/(dt)(5e^tcos(t)) ?
The first d/(dt)(5e^tcos(t)) is 5(e^tcos(t)-e^tsin(t))