What is the d/(dt)(e^{4t}sin(t)) ?

The d/(dt)(e^{4t}sin(t)) is e^{4t}*4sin(t)+cos(t)e^{4t}

What is the first d/(dt)(e^{4t}sin(t)) ?

The first d/(dt)(e^{4t}sin(t)) is e^{4t}*4sin(t)+cos(t)e^{4t}

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\frac{d}{d t} (e^{4 t} sin (t))

e^{4 t} \cdot 4 sin (t) + cos (t) e^{4 t}

Solution steps

\frac{d}{d t} (e^{4 t} sin (t))

Apply the Product Rule:

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

f = e^{4 t}, g = sin (t)

= \frac{d}{d t} (e^{4 t}) sin (t) + \frac{d}{d t} (sin (t)) e^{4 t}

\frac{d}{d t} (e^{4 t}) = e^{4 t} \cdot 4

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

= e^{4 t} \cdot 4 sin (t) + cos (t) e^{4 t}

What is the d/(dt)(e^{4t}sin(t)) ?
The d/(dt)(e^{4t}sin(t)) is e^{4t}*4sin(t)+cos(t)e^{4t}
What is the first d/(dt)(e^{4t}sin(t)) ?
The first d/(dt)(e^{4t}sin(t)) is e^{4t}*4sin(t)+cos(t)e^{4t}