{"id":8647,"date":"2012-04-22T22:55:44","date_gmt":"2012-04-22T21:55:44","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8647"},"modified":"2021-12-30T23:27:04","modified_gmt":"2021-12-30T23:27:04","slug":"determine-a-expressao-designatoria-da-funcao-derivada","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8647","title":{"rendered":"Determine a express\u00e3o designat\u00f3ria da fun\u00e7\u00e3o derivada"},"content":{"rendered":"<p><ul id='GTTabs_ul_8647' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8647' class='GTTabs_curr'><a  id=\"8647_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8647' ><a  id=\"8647_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_8647'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determine a express\u00e3o designat\u00f3ria da fun\u00e7\u00e3o derivada de cada uma das fun\u00e7\u00f5es:<\/p>\n<ol>\n<li>$f:x \\to 2\\operatorname{sen} x + 5$<\/li>\n<li>$g:t \\to t &#8211; 2\\operatorname{sen} t$<\/li>\n<li>$h:\\theta\u00a0 \\to {\\theta ^2}\\operatorname{sen} \\theta $<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8647' onClick='GTTabs_show(1,8647)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8647'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{f'(x)}&amp; = &amp;{\\left( {2\\operatorname{sen} x + 5} \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{2 \\times \\left( {\\operatorname{sen} x} \\right)&#8217; + 0} \\\\<br \/>\n{}&amp; = &amp;{2\\cos x}<br \/>\n\\end{array}$$<br \/>\n\u00ad<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{g'(t)}&amp; = &amp;{\\left( {t &#8211; 2\\operatorname{sen} t} \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{t&#8217; &#8211; 2 \\times \\left( {\\operatorname{sen} t} \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{1 &#8211; 2\\cos t}<br \/>\n\\end{array}$$<br \/>\n\u00ad<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{h'(\\theta )}&amp; = &amp;{\\left( {{\\theta ^2}\\operatorname{sen} \\theta } \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{\\left( {{\\theta ^2}} \\right)&#8217; \\times \\operatorname{sen} \\theta\u00a0 + {\\theta ^2} \\times \\left( {\\operatorname{sen} \\theta } \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{2\\theta \\operatorname{sen} \\theta\u00a0 + {\\theta ^2}\\cos \\theta }<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8647' onClick='GTTabs_show(0,8647)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determine a express\u00e3o designat\u00f3ria da fun\u00e7\u00e3o derivada de cada uma das fun\u00e7\u00f5es: $f:x \\to 2\\operatorname{sen} x + 5$ $g:t \\to t &#8211; 2\\operatorname{sen} t$ $h:\\theta\u00a0 \\to {\\theta ^2}\\operatorname{sen} \\theta $ Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19178,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[226,97,267],"tags":[427,136,307],"series":[],"class_list":["post-8647","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-exponenciais-e-logaritmicas","tag-12-o-ano","tag-derivada","tag-funcoes-trigonometricas"],"views":6266,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat69.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8647","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8647"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8647\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8647"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8647"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8647"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}