Buscar Volver arriba Filtrar resultadosUbicaciónMatemáticas (2)ClasificaciónTipo de artículoCategoríaGuíaTemaN/AN/AAuthorRebecca Laff & Wendy RuizParis, Ricardo, Raymond, & JohnsonJennifer Paris, Kristin Beeve, & Clint SpringerKrischa Esquivel, Emily Elam, Jennifer Paris, & Maricela TafoyaIrma Isabel González CuadrosJoaquín López HerraizMaría M. Reynoso, Carina E. Magnoli, Germán G. Barros y Mirta S. DemoGlencora BorradaileShow TOCyesnoCover PageyesTOC OnlyCompile but don't publishLicensePublic DomainCC BYCC BY-SACC BY-NC-SACC BY-NDCC BY-NC-NDGNU GPLAll Rights ReservedCC BY-NCGNU FDLTranscludedAutonumber Section Headingstitle with space delimiterstitle with colon delimiterstitle with dash delimitersLicense Version1.01.32.02.53.04.0Incluir datos adjuntosTipo de contenidoDocumentoImagenOtro Buscando enTodos los resultadosAcerca de 2 resultados6.3: Diferenciación complejahttps://espanol.libretexts.org/Matematicas/Algebra_lineal/Libro%3A_An%C3%A1lisis_Matriz_(Cox)/06%3A_An%C3%A1lisis_Complejo_I/6.03%3A_Diferenciaci%C3%B3n_compleja\[\begin{align*} \lim z \rightarrow z_{0} \frac{z^2-z_{0}^2}{z-z_{0}} &= \lim_{z \rightarrow z_{0}} \frac{(z-z_{0})(z+z_{0})}{z-z_{0}} \\[4pt] &= 2z_{0} \end{align*}\] \[\begin{align*} \lim z \rightar...\[\begin{align*} \lim z \rightarrow z_{0} \frac{z^2-z_{0}^2}{z-z_{0}} &= \lim_{z \rightarrow z_{0}} \frac{(z-z_{0})(z+z_{0})}{z-z_{0}} \\[4pt] &= 2z_{0} \end{align*}\] \[\begin{align*} \lim z \rightarrow z_{0} \frac{e^{z}-e^{z_{0}}}{z-z_{0}} &= e^{z_{0}} \lim_{z \rightarrow z_{0}} \frac{e^{z-z_{0}}-1}{z-z_{0}} \\[4pt] &= e^{z_{0}} \lim_{z \rightarrow z_{0}} \sum_{n = 0}^{\infty} \frac{(z-z_{0})^{n}}{(n+1)!} \\[4pt] &= e^{z_{0}} \end{align*}\]Más2.5: Derivadoshttps://espanol.libretexts.org/Matematicas/Analisis/Variables_complejas_con_aplicaciones_(Orloff)/02%3A_Funciones_anal%C3%ADticas/2.05%3A_Derivados\[\begin{array} {rcl} {\dfrac{d}{dz} (f(z) g(z))} & = & {\lim_{z \to z_0} \dfrac{f(z) g(z) - f(z_0) g(z_0)}{z - z_0}} \\ {} & = & {\lim_{z \to z_0} \dfrac{(f(z) - f(z_0)) g(z) + f(z_0) (g(z) - g(z_0))...\[\begin{array} {rcl} {\dfrac{d}{dz} (f(z) g(z))} & = & {\lim_{z \to z_0} \dfrac{f(z) g(z) - f(z_0) g(z_0)}{z - z_0}} \\ {} & = & {\lim_{z \to z_0} \dfrac{(f(z) - f(z_0)) g(z) + f(z_0) (g(z) - g(z_0))}{z - z_0}} \\ {} & = & {\lim_{z \to z_0} \dfrac{f(z) - f(z_0)}{z - z_0} g(z) + f(z_0) \dfrac{(g(z) - g(z_0))}{z - z_0}} \\ {} & = & {f'(z_0) g(z_0) + f(z_0) g'(z_0)} \end{array}\]MásMostrar más resultados
