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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int \frac{arcsin ( 7 x )}{1 - 49 x ^{2}} d x

ln (\frac{5}{x ^{2}})

x^{2} y = 4, x = 2, y = 4

9 cos (- x)

\int \frac{1}{x ^{2} + 8 x} d x

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