Differentiating y: Product Rule Applied

[bubbles]

Homework Statement

Differentiate y = u * e^t + v * t * e^t

Homework Equations

Product Rule.

The Attempt at a Solution

y = u' * e^t + u * e^t + ( v' * t * e^t + v * e^t + v * t * e^t)

u and v are functions of t.

I forgot whether the product rule works like this: d/dt [xyz] = x'yz + xy'z + xyz' when x, y, z are all functions of t. Is this correct?

 

[Tedjn]

Yes, that's correct.