{"id":28206,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/why-is-derivative-of-constant-zero"},"modified":"2017-08-12T07:11:32","modified_gmt":"2017-08-12T07:11:32","slug":"why-is-derivative-of-constant-zero","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/why-is-derivative-of-constant-zero\/","title":{"rendered":"Why is derivative of constant zero?"},"content":{"rendered":"<p>Use the limit definition of the derivative:<\/p>\n<p>##f'(x)=lim_(hrarr0)(f(x+h)-f(x))\/h##<\/p>\n<p>If ##f(x)=&#8221;C&#8221;##, where ##&#8221;C&#8221;## is any constant, then<\/p>\n<p>##f(x+h)=&#8221;C&#8221;##<\/p>\n<p>Thus,<\/p>\n<p>##f'(x)=lim_(hrarr0)(&#8220;C&#8221;-&#8220;C&#8221;)\/h=lim_(hrarr0)0\/h=lim_(hrarr0)0=0## <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Use the limit definition of the derivative: ##f'(x)=lim_(hrarr0)(f(x+h)-f(x))\/h## If ##f(x)=&#8221;C&#8221;##, where ##&#8221;C&#8221;## is any constant, then ##f(x+h)=&#8221;C&#8221;## Thus, ##f'(x)=lim_(hrarr0)(&#8220;C&#8221;-&#8220;C&#8221;)\/h=lim_(hrarr0)0\/h=lim_(hrarr0)0=0##<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-28206","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/28206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=28206"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/28206\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=28206"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=28206"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=28206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}