# Differentiation rules

• Robert Gilbert
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)

## Abstract

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).

## Keywords

Inverse Function Product Rule Chain Rule Differentiation Rule Implicit Relation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.