{"id":590,"date":"2016-11-18T07:00:43","date_gmt":"2016-11-18T12:00:43","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=590"},"modified":"2026-04-04T11:28:55","modified_gmt":"2026-04-04T16:28:55","slug":"tabla-de-derivadas","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-recursos\/tabla-de-derivadas\/","title":{"rendered":"Tabla de derivadas"},"content":{"rendered":"

Referencia:<\/strong> Leon W Couch Ap\u00e9ndice p656<\/p>\n

Tabla de Derivadas<\/h3>\n

Definici\u00f3n<\/p>\n \\frac{d}{dx}[ f(x) ]= \\lim_{\\Delta x \\rightarrow\\ 0} \\frac{f \\big( x+\\frac{\\Delta x}{2} \\big)- f\\big( x-\\frac{\\Delta x}{2}\\big) }{\\Delta x} <\/span>\n

Regla del producto<\/p>\n \\frac{d}{dx}[u(x) v(x)]= u(x)\\frac{dv(x)}{dx} + v(x)\\frac{du(x)}{dx} <\/span>\n

Regla del cociente<\/p>\n \\frac{d}{dx} \\left[ \\frac{u(x)}{v(x)}\\right] = \\frac{1}{v^2(x)} \\left[ v(x)\\frac{du(x)}{dx}- u(x)\\frac{dv(x)}{dx}\\right] <\/span>\n

Regla de la cadena<\/p>\n \\frac{d}{dx}u[v(x)]= \\frac{du}{dv}\\frac{dv}{dx} <\/span>\n

Potenciaci\u00f3n<\/p>\n \\frac{d}{dx}[ x^n ]= nx^{n-1} <\/span>\n

Exponenciales<\/p>\n \\frac{d}{dx} [ e ^{ax} ] = a e^{ax} <\/span>\n \\frac{d}{dx} [ a ^{x} ]= a^x ln(a) <\/span>\n

Logaritmicas<\/p>\n \\frac{d}{dx} [ ln(x) ] = \\frac{1}{x} <\/span>\n \\frac{d}{dx}[ log_a (x) ] = \\frac{1}{x} log_a e <\/span>\n

Trigonom\u00e9tricas<\/p>\n \\frac{d}{dx}[sen(ax)]= a\\text{ } cos(ax) <\/span>\n \\frac{d}{dx}[cos(ax)]= -a\\text{ }sen(ax) <\/span>\n \\frac{d}{dx}[tan(ax)]= \\frac{a} {cos^2(ax)} <\/span>\n \\frac{d}{dx}[sen^{-1}(ax)]= \\frac{a} {\\sqrt{1-(ax)^2}} <\/span>\n \\frac{d}{dx}[cos^{-1}(ax)]= \\frac{-a} {\\sqrt{1-(ax)^2}} <\/span>\n \\frac{d}{dx}[tan^{-1}(ax)]= \\frac{a} {{1+(ax)^2}} <\/span>\n

\n

Regla de Leibniz<\/p>\n

\\frac{d}{dx}\\left[ \\int_{a(x)}^{b(x)} f(\\lambda,x) d\\lambda \\right] = <\/span>
\n = f(b(x),x) \\frac{d}{dx}[b(x)] - f(a(x),x) \\frac{d}{dx}[a(x)] + <\/span>
\n + \\int_{a(x)}^{b(x)} \\frac{d}{dx}[f(\\lambda , x) d\\lambda <\/span><\/p>\n

\n","protected":false},"excerpt":{"rendered":"

Referencia: Leon W Couch Ap\u00e9ndice p656 Tabla de Derivadas Definici\u00f3n Regla del producto Regla del cociente Regla de la cadena Potenciaci\u00f3n Exponenciales Logaritmicas Trigonom\u00e9tricas Regla de Leibniz<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-stp-unidades","format":"standard","meta":{"footnotes":""},"categories":[205],"tags":[],"class_list":["post-590","post","type-post","status-publish","format-standard","hentry","category-stp-recursos"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/590","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=590"}],"version-history":[{"count":1,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/590\/revisions"}],"predecessor-version":[{"id":22281,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/590\/revisions\/22281"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=590"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=590"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}