Abstract
If f is differentiable, its derivative f′ can be computed using the limit (4.11),
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).
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© 2002 Springer-Verlag Wien
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Ben-Israel, A., Gilbert, R. (2002). Differentiation rules. In: Computer-Supported Calculus. Texts and Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6146-3_5
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DOI: https://doi.org/10.1007/978-3-7091-6146-3_5
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-7230-8
Online ISBN: 978-3-7091-6146-3
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