Calculating the Derivative of U(t)y: DE for Dummies Ch. 2

[Storm Butler]

Homework Statement

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

Homework 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 don't know if that helps at all.

The Attempt at a Solution

The reason i don't understand it is because if i were to take the derivative of U(t)*y which I am 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)

 

[Cyosis]

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.