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2: Derivados

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    La derivada de una función\(f\) es otra función\(f'\),, definida como\[f'(x) \;\equiv\; \frac{df}{dx} \;\equiv\; \lim_{\delta x \rightarrow 0} \, \frac{f(x + \delta x) - f(x)}{\delta x}.\] Este tipo de expresión se denomina expresión limit porque implica un límite (en este caso, el límite donde\(\delta x\) va a cero).

    Si la derivada existe dentro de algún dominio de\(x\) (es decir, la expresión límite anterior está matemáticamente bien definida), entonces decimos que\(f\) es diferenciable en ese dominio. Se puede demostrar que una función diferenciable es automáticamente continua.

    Gráficamente, la derivada representa la pendiente de la gráfica de\(f(x)\), como se muestra a continuación:

    clipboard_ed2de0f8c8a5504571c253e11b33a039d.png
    Figura\(\PageIndex{1}\)

    Si\(f\) es diferenciable, podemos definir su derivada de segundo orden\(f''\) como la derivada de\(f'\). Los derivados de tercer orden y de orden superior se definen de manera similar.


    This page titled 2: Derivados is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Y. D. Chong via source content that was edited to the style and standards of the LibreTexts platform.