{"id":369,"date":"2023-07-03T20:49:06","date_gmt":"2023-07-03T20:49:06","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%ba%bf%e6%80%a7%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0\/"},"modified":"2023-07-03T20:49:06","modified_gmt":"2023-07-03T20:49:06","slug":"%e7%ba%bf%e6%80%a7%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%ba%bf%e6%80%a7%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0\/","title":{"rendered":"\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u5411\u60a8\u5c55\u793a\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u662f\u591a\u5c11\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u6c42\u89e3\u4e86\u7ebf\u6027\u51fd\u6570\u5bfc\u6570\u7684\u51e0\u4e2a\u793a\u4f8b\uff0c\u5e76\u6f14\u793a\u4e86\u6b64\u7c7b\u5bfc\u6570\u7684\u516c\u5f0f\u3002\u60a8\u751a\u81f3\u53ef\u4ee5\u627e\u5230\u6709\u5173\u7ebf\u6027\u51fd\u6570\u5bfc\u6570\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-de-una-funcion-lineal\"><\/span>\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u662f\u4ec0\u4e48\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u662f\u4e00\u6b21\u9879 \u7684\u7cfb\u6570<\/strong>\uff0c\u4e5f\u5c31\u662f\u8bf4\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570<em>f(x)=Ax+B<\/em>\u7b49\u4e8e<em>A\u3002<\/em><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da354d71cc8fcc91ec98275630d162d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=Ax+B\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=A\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"352\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u5e38\u6570\u7684\u5bfc\u6570\/\">\u5e38\u6570\u7684\u5bfc\u6570<\/a><\/span>\u4e3a\u96f6\uff0c\u56e0\u6b64\u4ece\u5bfc\u6570\u4e2d\u5220\u9664\u4e86\u72ec\u7acb\u9879\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u4e00\u6b21\u9879\u7684\u5bfc\u6570\u662f\u6240\u8ff0\u9879\u7684\u7cfb\u6570\u3002\u56e0\u6b64\uff0c\u8fd9\u4e24\u7c7b\u51fd\u6570\u4e4b\u548c\u7684\u5bfc\u6570\u5c31\u662f\u7ebf\u6027\u9879\u7684\u7cfb\u6570\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-dune-fonction-lineaire.webp\" alt=\"\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\" class=\"wp-image-1739\" width=\"263\" height=\"224\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4ece\u51e0\u4f55\u89d2\u5ea6\u6765\u8bf4\uff0c\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u5c31\u662f\u8be5\u51fd\u6570\u7684\u659c\u7387\u3002\u5728\u4e0a\u56fe\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u8868\u793a\u4e00\u4e2a\u7ebf\u6027\u51fd\u6570\u53ca\u5176\u5bfc\u6570\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-funciones-lineales\"><\/span>\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u51fa\u7ebf\u6027\u51fd\u6570\u5bfc\u6570\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97\u51e0\u4e2a\u7ebf\u6027\u51fd\u6570\u7684\u4f8b\u5b50\u6765\u5b8c\u6210\u5bf9\u6982\u5ff5\u7684\u7406\u89e3\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b12cfa0a6432f8171149ec0139d259ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=3x+1\\quad\\longrightarrow\\quad f'(x)=3\\\\[3ex]f(x)=5x-4\\quad\\longrightarrow\\quad f'(x)=5\\\\[3ex] f(x)=-2x+9\\quad\\longrightarrow\\quad f'(x)=-2\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"280\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u5f53\u51fd\u6570\u6ca1\u6709\u72ec\u7acb\u9879\u65f6\uff0c\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u5982\u679c\u5b83\u53ea\u6709\u4e00\u4e2a\u4e00\u7ea7\u9879\uff0c\u5219\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u59cb\u7ec8\u662f\u4f34\u968f\u53d8\u91cf x \u7684\u6570\u5b57\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01c42c8e73ed47d26a090c027af24e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=8x\\quad\\longrightarrow\\quad f'(x)=8\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"223\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u662f\u4e00\u4e2a\u6ca1\u6709\u81ea\u53d8\u91cf\u7684\u51fd\u6570\uff0c\u4e00\u4e2a\u7b80\u5355\u7684\u6570\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-derivada-de-una-funcion-lineal\"><\/span>\u7ebf\u6027\u51fd\u6570\u5bfc\u6570\u7684\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u6f14\u793a\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u516c\u5f0f\u3002<\/p>\n<p>\u4ee4<em>f \u4e3a<\/em>\u4efb\u610f\u7ebf\u6027\u51fd\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-370811a2aa0db8d9ec651bc54ec64e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=Ax+B\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97\u51fd\u6570\u5728\u4e00\u70b9\u7684\u5bfc\u6570\u7684\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1162892842eac60784851f1e85e8fdb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(a)=\\lim_{h\\to 0}\\frac{f(a+h)-f(a)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"217\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u8ba1\u7b97\u7ebf\u6027\u51fd\u6570\u7684\u524d\u6781\u9650\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82bb6155f8feedee8ffd37d7d721be41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(a)=\\lim_{h\\to 0}\\frac{f(a+h)-f(a)}{h}=\\frac{A(a+h)+B-(A\\cdot a+B)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"456\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u89e3\u6790\u62ec\u53f7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fad6e047e98d5201667c8605457c08f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(a)=\\frac{Aa+Ah+B-Aa-B}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"249\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u7528\u5206\u5b50\u6765\u8fd0\u7b97\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a65d5b69a49d803b5347d019191a4500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(a)=\\frac{Ah}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"88\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u7b80\u5316\u5206\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33d6b2531eeda784111d43aca63830d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(a)=A\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u603b\u4e4b\uff0c\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u7b49\u4e8e\u4efb\u610f\u70b9\u7684\u4e00\u6b21\u9879\u7684\u7cfb\u6570\u3002\u7531\u6b64\uff0c\u5bfc\u51fa\u4e86\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u516c\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-derivadas-de-funciones-lineales\"><\/span>\u89e3\u51b3\u4e86\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7eaaec94975c0a6f735ed64a9f4c8559_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)}\\ f(x)=2x-25\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b6d868f61cd6a9508bd6d32040c4b0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)}\\ f(x)=x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-558f5203bb08cc856a3b3f6e5ba06880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)}\\ f(x)=-9x-1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc3b5146a38b0ca48d55e02fe3318f07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)}\\ f(x)=\\cfrac{1}{2}x+7\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"136\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-47708f79ca9b8e2aef23d88e5137467a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)}\\ f(x)=5x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-198f38dc1105d5d3a1787a414f5b1619_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)}\\ f(x)=\\sqrt{7}x+\\frac{3}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"147\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u5bfc\u51fa\u7ebf\u6027\u51fd\u6570\uff0c\u53ea\u9700\u4ece\u51fd\u6570\u4e2d\u6d88\u9664\u5e38\u6570\u9879\u548c\u53d8\u91cf\uff0c\u4ec5\u4fdd\u7559\u7ebf\u6027\u9879\u7684\u7cfb\u6570\u3002\u7136\u800c\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-162a6c1b0989828157ac2bba886b4dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)}\\ f'(x)=2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7e751128f71b2780e6c74982ba17b8da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)}\\ f'(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-745a8ca29575777f5ed665282b33ba5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)}\\ f'(x)=-9\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-851faa652678a22b7aa681ef83544459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)}\\ f'(x)=\\cfrac{1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"100\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a2874e7133b50fc9e7dd628a35296a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)}\\ f'(x)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1887bdd187bb5bcf860a6a8692de2660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)}\\ f'(x)=\\sqrt{7}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5c3d\u7ba1\u51fd\u6570\u7684\u7cfb\u6570\u662f\u5206\u6570\u6216\u6839\uff0c\u4f46\u7ebf\u6027\u51fd\u6570\u7684\u63a8\u5bfc\u662f\u4ee5\u76f8\u540c\u7684\u65b9\u5f0f\u5b8c\u6210\u7684\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u5411\u60a8\u5c55\u793a\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570\u662f\u591a\u5c11\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u6c42\u89e3\u4e86\u7ebf\u6027\u51fd\u6570\u5bfc\u6570\u7684\u51e0\u4e2a\u793a\u4f8b\uff0c\u5e76\u6f14\u793a\u4e86\u6b64\u7c7b\u5bfc\u6570\u7684\u516c\u5f0f &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%ba%bf%e6%80%a7%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[6],"tags":[],"class_list":["post-369","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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