# Math Help - Is it true that...? (Derivative Question)

1. ## Is it true that...? (Derivative Question)

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!

2. $y = e^u(\cos(u)+cu)$

I expand and use the product rule.

$y = e^u\cos(u)+e^ucu$

$\frac{dy}{du} = e^u\cos(u)- e^u\sin(u)+e^ucu+ce^u$

$\frac{dy}{du} = e^u(\cos(u)-\sin(u)+cu+c)$