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A.3: Tabla de Derivados

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    118875
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    A lo largo de esta tabla,\(a\) y\(b\) son constantes, independientes de\(x\text{.}\)

    \(F(x)\) \(F'(x)=\frac{\mathrm{d}F}{\mathrm{d}x}\)
    \(af(x)+bg(x)\) \(af'(x)+bg'(x)\)
    \(f(x)+g(x)\) \(f'(x)+g'(x)\)
    \(f(x)-g(x)\) \(f'(x)-g'(x)\)
    \(af(x)\) \(af'(x)\)
    \(f(x)g(x)\) \(f'(x)g(x)+f(x)g'(x)\)
    \(f(x)g(x)h(x)\) \(f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)\)
    \(\frac{f(x)}{g(x)}\) \(\frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}\)
    \(\frac{1}{g(x)}\) \(-\frac{g'(x)}{g(x)^2}\)
    \(f\big(g(x)\big)\) \(f'\big(g(x)\big)g'(x)\)

     

    \(F(x)\) \(F'(x)=\frac{\mathrm{d}F}{\mathrm{d}x}\)
    \(a\) \(0\)
    \(x^a\) \(ax^{a-1}\)
    \(g(x)^a\) \(ag(x)^{a-1}g'(x)\)
    \(\sin x\) \(\cos x\)
    \(\sin g(x)\) \(g'(x)\cos g(x)\)
    \(\cos x\) \(-\sin x\)
    \(\cos g(x)\) \(-g'(x)\sin g(x)\)
    \(\tan x\) \(\sec^2 x\)
    \(\csc x\) \(-\csc x\cot x\)
    \(\sec x\) \(\sec x\tan x\)
    \(\cot x\) \(-\csc^2 x\)
    \(e^x\) \(e^x\)
    \(e^{g(x)}\) \(g'(x)e^{g(x)}\)
    \(a^x\) \((\ln a)\ a^x\)

     

    \(F(x)\) \(F'(x)=\frac{\mathrm{d}F}{\mathrm{d}x}\)
    \(\ln x\) \(\frac{1}{x}\)
    \(\ln g(x)\) \(\frac{g'(x)}{g(x)}\)
    \(\log_a x\) \(\frac{1}{x\ln a}\)
    \(\arcsin x\) \(\frac{1}{\sqrt{1-x^2}}\)
    \(\arcsin g(x)\) \(\frac{g'(x)}{\sqrt{1-g(x)^2}}\)
    \(\arccos x\) \(-\frac{1}{\sqrt{1-x^2}}\)
    \(\arctan x\) \(\frac{1}{1+x^2}\)
    \(\arctan g(x)\) \(\frac{g'(x)}{1+g(x)^2}\)
    \(\textrm{arccsc} x\) \(-\frac{1}{|x|\sqrt{x^2-1}}\)
    \(\textrm{arcsec} x\) \(\frac{1}{|x|\sqrt{x^2-1}}\)
    \(\textrm{arccot} x\) \(-\frac{1}{1+x^2}\)

    This page titled A.3: Tabla de Derivados is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Joel Feldman, Andrew Rechnitzer and Elyse Yeager via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.