# Homework Help: Im confused by this derivative (problem taken from differential equations for dummies

1. Jul 6, 2009

### Storm Butler

1. The problem statement, all variables and given/known data

The derivative comes from a step in solving a differential equation from the book differential equations for dummies. (if anyone has the book it is in the second chapter page 27).

d[U(t) y]/dt=U(t) dy/dt+ dU(t) y/dt

2. Relevant equations

The original differential that was trying to be solved was dy/dt+2y=4 and he was trying to find the integrating factor, i dont know if that helps at all.

3. The attempt at a solution

The reason i dont understand it is because if i were to take the derivative of U(t)*y which im pretty sure is what it is asking i would think that it would simply be the derivative of U(t) times y (dt/dy= U'(t)*y)

2. Jul 6, 2009

### Cyosis

Re: Im confused by this derivative (problem taken from differential equations for dum

If y would be constant with respect to time your original differential equation would be somewhat trivial wouldn't it be? It would probably not even have a solution. The function you're differentiating is this:

$$\frac{d U(t)y(t)}{d t}$$

Use the product rule.