Document Zbl 1145.26301

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Bootstrapping our way to the product rule. (English) Zbl 1145.26301

Missouri J. Math. Sci. 19, No. 3, 195-199 (2007).

Summary: A technique is introduced for proving the product rule for the differentiation of the product of two functions in an undergraduate real analysis class. The general form of the product rule is proved using the sum rule and constant multiple rule as well as a special case of the product rule. This special case can be proved quite easily using only the definition of the derivative and the fact that a differentiable function is continuous.

MSC:

26A06	One-variable calculus
26A24	Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
97D40	Mathematics teaching methods and classroom techniques

Keywords:

undergraduate real analysis

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