2002 | OriginalPaper | Buchkapitel
Differentiation rules
verfasst von : Dr. Adi Ben-Israel, Dr. Robert Gilbert
Erschienen in: Computer-Supported Calculus
Verlag: Springer Vienna
Enthalten in: Professional Book Archive
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If f is differentiable, its derivative f′ can be computed using the limit (4.11), $$f'\left( x \right) = \mathop {\lim }\limits_{\xi \to x} {\rm{ }}{{f\left( \xi \right) - f\left( x \right)} \over {\xi - x}},$$ which is often difficult. However, sometimes f has a special structure that allows differentiating it without evaluating the limit (4.11). For example, if u and v are differentiable functions, and if f is their product f = uv, then the derivative f′ can be easily computed from the derivatives u′ and v′ . This situation is covered by a differentiation rule called the product rule (Theorem 5.1). Other rules given in this chapter are the quotient rule (Theorem 5.5) and the chain rule (Theorem 5.11).