A.3: Tabla de Derivados
- Page ID
- 119231
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)A lo largo de esta tabla,\(a\) y\(b\) son constantes, independientes de\(x\text{.}\)
| \(F(x)\) | \(F'(x)=\dfrac{dF}{dx}\) |
| \(af(x)+bg(x)\) | \(af'(x)+bg'(x)\) |
| \(f(x)+g(x)\) | \(f'(x)+g'(x)\) |
| \(f(x)-g(x)\) | \(f'(x)-g'(x)\) |
| \(af(x)\) | \(af'(x)\) |
| \(f(x)g(x)\) | \(f'(x)g(x)+f(x)g'(x)\) |
| \(f(x)g(x)h(x)\) | \(f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)\) |
| \(\frac{f(x)}{g(x)}\) | \(\frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}\) |
| \(\frac{1}{g(x)}\) | \(-\frac{g'(x)}{g(x)^2}\) |
| \(f\big(g(x)\big)\) | \(f'\big(g(x)\big)g'(x)\) |
| \(F(x)\) | \(F'(x)=\dfrac{dF}{dx}\) |
| \(a\) | \(0\) |
| \(x^a\) | \(ax^{a-1}\) |
| \(g(x)^a\) | \(ag(x)^{a-1}g'(x)\) |
| \(\sin x\) | \(\cos x\) |
| \(\sin g(x)\) | \(g'(x)\cos g(x)\) |
| \(\cos x\) | \(-\sin x\) |
| \(\cos g(x)\) | \(-g'(x)\sin g(x)\) |
| \(\tan x\) | \(\sec^2 x\) |
| \(\csc x\) | \(-\csc x\cot x\) |
| \(\sec x\) | \(\sec x\tan x\) |
| \(\cot x\) | \(-\csc^2 x\) |
| \(e^x\) | \(e^x\) |
| \(e^{g(x)}\) | \(g'(x)e^{g(x)}\) |
| \(a^x\) | \((\ln a)\ a^x\) |
| \(F(x)\) | \(F'(x)=\dfrac{dF}{dx}\) |
| \(\ln x\) | \(\frac{1}{x}\) |
| \(\ln g(x)\) | \(\frac{g'(x)}{g(x)}\) |
| \(\log_a x\) | \(\frac{1}{x\ln a}\) |
| \(\arcsin x\) | \(\frac{1}{\sqrt{1-x^2}}\) |
| \(\arcsin g(x)\) | \(\frac{g'(x)}{\sqrt{1-g(x)^2}}\) |
| \(\arccos x\) | \(-\frac{1}{\sqrt{1-x^2}}\) |
| \(\arctan x\) | \(\frac{1}{1+x^2}\) |
| \(\arctan g(x)\) | \(\frac{g'(x)}{1+g(x)^2}\) |
| \(\textrm{arccsc}\, x\) | \(-\frac{1}{|x|\sqrt{x^2-1}}\) |
| \(\textrm{arcsec}\, x\) | \(\frac{1}{|x|\sqrt{x^2-1}}\) |
| \(\textrm{arccot}\,x\) | \(-\frac{1}{1+x^2}\) |