Is it true that if y = e^u(cos(u)+cu) where c is a constant, then it's derivative is y' = e^u(-sin(u) + C) + e^u(cos(u) + Cu)? I listed them both below to more easily see them.

y = e^u(cos(u)+Cu)

y' = e^u(-sin(u) + C) + e^u(cos(u) + Cu)

Thanks, I'm just making sure I'm doing the product rule and such correctly!