Derivative of e^t sin(2t) using the product rule

[quicksilver123]

Mod note: Changed title from "Differential Euler's Number"
1. Homework Statement
Find the derivative.
f(t)=e^tsin2t

The Attempt at a Solution

f'(t)=e^tsin2t(sin2t)(cos2t)(2)

However the book seems to say that there should be an extra "t" in the solution. Some help?

 

[Mark44]

Homework Statement

Find the derivative.
f(t)=e^tsin2t

The Attempt at a Solution

f'(t)=e^tsin2t(sin2t)(cos2t)(2)

This is incorrect. It should be $f'(t) = e^{t\sin(2t)} \cdot \frac d{dt}(t \sin(2t))$
To get that last derivative you need to use the product rule and the chain rule, in that order.

However the book seems to say that there should be an extra "t" in the solution. Some help?

 

[quicksilver123]

Thank you!

I appreciate all of your help the past couple of days, for some reason I've been making a lot of mistakes but after a heavy study session today I'm feeling much more capable.

Thanks again!