A.3: Tabla de Derivados
- Page ID
- 119231
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A lo largo de esta tabla,\(a\) y\(b\) son constantes, independientes de\(x\text{.}\)
\(F(x)\) | \(F'(x)=\dfrac{dF}{dx}\) |
\(af(x)+bg(x)\) | \(af'(x)+bg'(x)\) |
\(f(x)+g(x)\) | \(f'(x)+g'(x)\) |
\(f(x)-g(x)\) | \(f'(x)-g'(x)\) |
\(af(x)\) | \(af'(x)\) |
\(f(x)g(x)\) | \(f'(x)g(x)+f(x)g'(x)\) |
\(f(x)g(x)h(x)\) | \(f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)\) |
\(\frac{f(x)}{g(x)}\) | \(\frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}\) |
\(\frac{1}{g(x)}\) | \(-\frac{g'(x)}{g(x)^2}\) |
\(f\big(g(x)\big)\) | \(f'\big(g(x)\big)g'(x)\) |
\(F(x)\) | \(F'(x)=\dfrac{dF}{dx}\) |
\(a\) | \(0\) |
\(x^a\) | \(ax^{a-1}\) |
\(g(x)^a\) | \(ag(x)^{a-1}g'(x)\) |
\(\sin x\) | \(\cos x\) |
\(\sin g(x)\) | \(g'(x)\cos g(x)\) |
\(\cos x\) | \(-\sin x\) |
\(\cos g(x)\) | \(-g'(x)\sin g(x)\) |
\(\tan x\) | \(\sec^2 x\) |
\(\csc x\) | \(-\csc x\cot x\) |
\(\sec x\) | \(\sec x\tan x\) |
\(\cot x\) | \(-\csc^2 x\) |
\(e^x\) | \(e^x\) |
\(e^{g(x)}\) | \(g'(x)e^{g(x)}\) |
\(a^x\) | \((\ln a)\ a^x\) |
\(F(x)\) | \(F'(x)=\dfrac{dF}{dx}\) |
\(\ln x\) | \(\frac{1}{x}\) |
\(\ln g(x)\) | \(\frac{g'(x)}{g(x)}\) |
\(\log_a x\) | \(\frac{1}{x\ln a}\) |
\(\arcsin x\) | \(\frac{1}{\sqrt{1-x^2}}\) |
\(\arcsin g(x)\) | \(\frac{g'(x)}{\sqrt{1-g(x)^2}}\) |
\(\arccos x\) | \(-\frac{1}{\sqrt{1-x^2}}\) |
\(\arctan x\) | \(\frac{1}{1+x^2}\) |
\(\arctan g(x)\) | \(\frac{g'(x)}{1+g(x)^2}\) |
\(\textrm{arccsc}\, x\) | \(-\frac{1}{|x|\sqrt{x^2-1}}\) |
\(\textrm{arcsec}\, x\) | \(\frac{1}{|x|\sqrt{x^2-1}}\) |
\(\textrm{arccot}\,x\) | \(-\frac{1}{1+x^2}\) |