What is the d/(dt)(e^{2t}sin(4t)) ?

The d/(dt)(e^{2t}sin(4t)) is e^{2t}*2sin(4t)+cos(4t)*4e^{2t}

What is the first d/(dt)(e^{2t}sin(4t)) ?

The first d/(dt)(e^{2t}sin(4t)) is e^{2t}*2sin(4t)+cos(4t)*4e^{2t}

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\frac{d}{d t} (e^{2 t} sin (4 t))

e^{2 t} \cdot 2 sin (4 t) + cos (4 t) \cdot 4 e^{2 t}

Solution steps

\frac{d}{d t} (e^{2 t} sin (4 t))

Apply the Product Rule:

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

f = e^{2 t}, g = sin (4 t)

= \frac{d}{d t} (e^{2 t}) sin (4 t) + \frac{d}{d t} (sin (4 t)) e^{2 t}

\frac{d}{d t} (e^{2 t}) = e^{2 t} \cdot 2

\frac{d}{d t} (sin (4 t)) = cos (4 t) \cdot 4

= e^{2 t} \cdot 2 sin (4 t) + cos (4 t) \cdot 4 e^{2 t}

2 x^{2} e^{x}

\frac{d}{d x} (x^{2} y^{2} z^{2})

(9.8) (5)

\int \frac{1}{25 + 4 x ^{2}} d x

\int \frac{sin ( x ) - 4}{cos ( x )} d x

What is the d/(dt)(e^{2t}sin(4t)) ?
The d/(dt)(e^{2t}sin(4t)) is e^{2t}*2sin(4t)+cos(4t)*4e^{2t}
What is the first d/(dt)(e^{2t}sin(4t)) ?
The first d/(dt)(e^{2t}sin(4t)) is e^{2t}*2sin(4t)+cos(4t)*4e^{2t}