Question

Any tips on when it's better to distribute and when it's better to differentiate in a function? When you have a funciton like f(x) = x squared (x-3) should you always distribute first before differentiating? Any tips on when to do which?

Answer 1

I've always worked with the rule of thumb that if it is simple to distribute then do so, otherwise just use the product rule. If it is simple to distribute then doing so will often be easier than the product rule.

One of the problems with this rule of thumb is that "simple" is in the eye of the beholder. So, I guess the real answer is that experience will tell you when it's best to distribute and when it's best to just product rule.

Note however that many instructors do have preferences so it might not be a bad idea to ask your instructor if he/she has any preferences about this. Some will ask that you don't distribute even when easy so you can get practice with the product rule for example.