What is the d/(dt)(e^tsin(9t)) ?

The d/(dt)(e^tsin(9t)) is e^tsin(9t)+cos(9t)*9e^t

What is the first d/(dt)(e^tsin(9t)) ?

The first d/(dt)(e^tsin(9t)) is e^tsin(9t)+cos(9t)*9e^t

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\frac{d}{d t} (e^{t} sin (9 t))

e^{t} sin (9 t) + cos (9 t) \cdot 9 e^{t}

Solution steps

\frac{d}{d t} (e^{t} sin (9 t))

Apply the Product Rule:

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

f = e^{t}, g = sin (9 t)

= \frac{d}{d t} (e^{t}) sin (9 t) + \frac{d}{d t} (sin (9 t)) e^{t}

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

\frac{d}{d t} (sin (9 t)) = cos (9 t) \cdot 9

= e^{t} sin (9 t) + cos (9 t) \cdot 9 e^{t}

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What is the d/(dt)(e^tsin(9t)) ?
The d/(dt)(e^tsin(9t)) is e^tsin(9t)+cos(9t)*9e^t
What is the first d/(dt)(e^tsin(9t)) ?
The first d/(dt)(e^tsin(9t)) is e^tsin(9t)+cos(9t)*9e^t