2 The Product Rule

# 2 The Product Rule - Next The Quotient Rule Up Derivatives...

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Next: The Quotient Rule Up: Derivatives: How to Find Previous: The Power Rule The Product Rule Okay, here is a key rule, a rule without which calculus would just be a case of goofing around with a pile of very simple functions. Suppose that we have a function h which is obtained by multiplying together two functions f and g . So h ( x ) = f ( x ) g ( x ). And silly us, we want to take the derivative of h . It's extremely tempting to say: , but unfortunately that would be WRONG! How do we know it's wrong? Well, we didn't waste the best years of our lives studying math for nothing. Besides, if we apply it when f ( x ) = x and g ( x ) = x , we get WHICH IS WRONG! We already know that not the same as 1. Instead, the correct answer is found by the following, the real, correct, How to Ace Calculus

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