What is the derivative of e^{3tsin(2t)} ?

The derivative of e^{3tsin(2t)} is e^{3tsin(2t)}*3(sin(2t)+2tcos(2t))

What is the first derivative of e^{3tsin(2t)} ?

The first derivative of e^{3tsin(2t)} is e^{3tsin(2t)}*3(sin(2t)+2tcos(2t))

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derivative of

e^{3 t s i n (2 t)}

e^{3 t s i n (2 t)} \cdot 3 (sin (2 t) + 2 t cos (2 t))

Solution steps

\frac{d}{d t} (e^{3 t s i n (2 t)})

Apply the chain rule:

e^{3 t s i n (2 t)} \frac{d}{d t} (3 t sin (2 t))

= e^{3 t s i n (2 t)} \frac{d}{d t} (3 t sin (2 t))

\frac{d}{d t} (3 t sin (2 t)) = 3 (sin (2 t) + 2 t cos (2 t))

= e^{3 t s i n (2 t)} \cdot 3 (sin (2 t) + 2 t cos (2 t))

What is the derivative of e^{3tsin(2t)} ?
The derivative of e^{3tsin(2t)} is e^{3tsin(2t)}*3(sin(2t)+2tcos(2t))
What is the first derivative of e^{3tsin(2t)} ?
The first derivative of e^{3tsin(2t)} is e^{3tsin(2t)}*3(sin(2t)+2tcos(2t))