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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.