Abstract
The differential quotient of a function y = f(x) at x 0 is equal to \( \mathop {\lim }\limits_{{\Delta x \to 0}} \frac{{f(x_{0} +\Delta x) - f(x_{0} )}}{{\Delta x}} \) if this limit exists and is finite. The derivative function of a function y = f(x) with respect to the variable x is another function of x denoted by the symbols \( y^{{\prime }} ,\dot{y},Dy,\frac{dy}{dx},f^{{\prime }} (x),Df(x) \), or \( \frac{df(x)}{dx} \), and its value for every x is equal to the limit of the quotient of the increment of the function Δy and the corresponding increment Δx for Δx → 0, if this limit exists.
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© 2015 Springer-Verlag Berlin Heidelberg
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Bronshtein, I.N., Semendyayev, K.A., Musiol, G., Mühlig, H. (2015). Differentiation. In: Handbook of Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46221-8_6
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DOI: https://doi.org/10.1007/978-3-662-46221-8_6
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