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Popular >

d/(dt)(e^{2t}cos(2t))

Solution

\frac{d}{d t} (e^{2 t} cos (2 t))

Solution

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

Solution steps

\frac{d}{d t} (e^{2 t} cos (2 t))

Apply the Product Rule:

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

f = e^{2 t}, g = cos (2 t)

= \frac{d}{d t} (e^{2 t}) cos (2 t) + \frac{d}{d t} (cos (2 t)) e^{2 t}

\frac{d}{d t} (e^{2 t}) = e^{2 t} \cdot 2

\frac{d}{d t} (cos (2 t)) = - sin (2 t) \cdot 2

= e^{2 t} \cdot 2 cos (2 t) + (- sin (2 t) \cdot 2) e^{2 t}

Simplify

= 2 e^{2 t} cos (2 t) - 2 e^{2 t} sin (2 t)

Graph

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Frequently Asked Questions (FAQ)

What is the d/(dt)(e^{2t}cos(2t)) ?
The d/(dt)(e^{2t}cos(2t)) is 2e^{2t}cos(2t)-2e^{2t}sin(2t)
What is the first d/(dt)(e^{2t}cos(2t)) ?
The first d/(dt)(e^{2t}cos(2t)) is 2e^{2t}cos(2t)-2e^{2t}sin(2t)