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Popular Calculus >

d/(dt)(e^{-t}sin(2t))

Solution

\frac{d}{d t} (e^{- t} sin (2 t))

Solution

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

Solution steps

\frac{d}{d t} (e^{- t} sin (2 t))

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Graph

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Frequently Asked Questions (FAQ)

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