## Cute Proofs: The Product Rule for Derivatives.

### November 3, 2010

There’s always a few calculus students who make the error of trying to take the derivative of and get . Of course, we know that this is not true in general, and the product rule for derivatives is as follows:

**Theorem (Product Rule)**. If are differentiable, then .

Given this formula, it’s a nice exercise for students to find out for which functions it is true that .