1.3: Definition of the Derivative

Differential Equations · LibreTexts

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    The derivative of the function \(y = f(x)\), denoted as \(f ′ (x)\) or \(dy/dx\), is defined as the slope of the tangent line to the curve \(y = f(x)\) at the point \((x, y)\). This slope is obtained by a limit, and is defined as \[\label{eq:1}f'(x)=\underset{h\to 0}{\lim}\frac{f(x+h)-f(x)}{h}\]

    This page titled 1.3: Definition of the Derivative was last modified on Fri, 05 Nov 2021 01:29:39 GMT and is shared under a CC BY 3.0 license and was authored, remixed, and/or curated by Jeffrey R. Chasnov via source content that was edited to the style and standards of the LibreTexts platform.