Product Rule

Product rule

The area is formed by the product of two sides u and v. Both are functions of t (possibly time). How is the rate of change of u and v linked to that of the product uv? Consider: - which sides are changing? - imagine a small change du in u and dv in v (say 0.1 but could be smaller). - what would the area of the strip be? - can you come up with a rule for the rate of change of uv with respect to t?