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

The d/(dt)(e^{-t}cos(t)) is -e^{-t}cos(t)-e^{-t}sin(t)

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

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

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

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