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The difference quotient is sometimes also called the Newton quotient [10] [12] [13] [14] (after Isaac Newton) or Fermat's difference quotient (after Pierre de Fermat ).
Discrete differential calculus is the study of the definition, properties, and applications of the difference quotient of a function. The process of finding the difference quotient is called differentiation.
Symmetric derivative. In mathematics, the symmetric derivative is an operation generalizing the ordinary derivative. It is defined as: [1] [2] The expression under the limit is sometimes called the symmetric difference quotient. [3] [4] A function is said to be symmetrically differentiable at a point x if its symmetric derivative exists at that ...
A finite difference is a mathematical expression of the form f (x + b) ā f (x + a). If a finite difference is divided by b ā a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary ...
In principle, the derivative of a function can be computed from the definition by considering the difference quotient and computing its limit. Once the derivatives of a few simple functions are known, the derivatives of other functions are more easily computed using rules for obtaining derivatives of more complicated functions from simpler ones.
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The latter is the difference quotient for g at a, and because g is differentiable at a by assumption, its limit as x tends to a exists and equals gā² (a) . As for Q(g(x)), notice that Q is defined wherever f is.
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