What is the d/(dt)(e^{6tsin(2t)}) ?

The d/(dt)(e^{6tsin(2t)}) is e^{6tsin(2t)}*6(sin(2t)+2tcos(2t))

What is the first d/(dt)(e^{6tsin(2t)}) ?

The first d/(dt)(e^{6tsin(2t)}) is e^{6tsin(2t)}*6(sin(2t)+2tcos(2t))

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\frac{d}{d t} (e^{6 t s i n (2 t)})

e^{6 t s i n (2 t)} \cdot 6 (sin (2 t) + 2 t cos (2 t))

Solution steps

\frac{d}{d t} (e^{6 t s i n (2 t)})

Apply the chain rule:

e^{6 t s i n (2 t)} \frac{d}{d t} (6 t sin (2 t))

= e^{6 t s i n (2 t)} \frac{d}{d t} (6 t sin (2 t))

\frac{d}{d t} (6 t sin (2 t)) = 6 (sin (2 t) + 2 t cos (2 t))

= e^{6 t s i n (2 t)} \cdot 6 (sin (2 t) + 2 t cos (2 t))

What is the d/(dt)(e^{6tsin(2t)}) ?
The d/(dt)(e^{6tsin(2t)}) is e^{6tsin(2t)}*6(sin(2t)+2tcos(2t))
What is the first d/(dt)(e^{6tsin(2t)}) ?
The first d/(dt)(e^{6tsin(2t)}) is e^{6tsin(2t)}*6(sin(2t)+2tcos(2t))