Question

Let's derive this exponential function!

e^ (8t sin 2t)

I know the answer is e^ (8t sin 2t) * (8t sin 2t)'

I would love to go step by step to understand how to derive the exponent.

Thank you!

Answer 1

d(e^(8t sin 2t) / dt = (8t * 2cos 2t + 8sin 2t)e^(8t sin 2t) = (16t cos 2t + 8sin 2t) e^(8t sin 2t)