{"id":8651,"date":"2012-04-22T23:06:57","date_gmt":"2012-04-22T22:06:57","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8651"},"modified":"2021-12-30T10:11:29","modified_gmt":"2021-12-30T10:11:29","slug":"calcule-a-derivada-de-cada-uma-das-funcoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8651","title":{"rendered":"Calcule a derivada de cada uma das fun\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_8651' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8651' class='GTTabs_curr'><a  id=\"8651_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8651' ><a  id=\"8651_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_8651'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Calcule a derivada de cada uma das fun\u00e7\u00f5es reais de vari\u00e1vel real:<\/p>\n<ol>\n<li>$f:x \\to 3 + 2\\cos x$<\/li>\n<li>$g:x \\to \\operatorname{sen} x + \\cos x$<\/li>\n<li>$h:t \\to \\operatorname{sen} t.\\cos t$<\/li>\n<li>$i:z \\to 3z\\cos z$<\/li>\n<li>$j:x \\to 3x\\operatorname{tg} x$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8651' onClick='GTTabs_show(1,8651)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8651'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{f'(x)}&amp; = &amp;{\\left( {3 + 2\\cos x} \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{2 \\times \\left( {\\cos x} \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 2\\operatorname{sen} x}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{g'(x)}&amp; = &amp;{\\left( {\\operatorname{sen} x + \\cos x} \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{\\left( {\\operatorname{sen} x} \\right)&#8217; + \\left( {\\cos x} \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{\\cos x &#8211; \\operatorname{sen} x}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{h'(t)}&amp; = &amp;{\\left( {\\operatorname{sen} t.\\cos t} \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{\\left( {\\operatorname{sen} t} \\right)&#8217; \\times \\cos t + \\operatorname{sen} t \\times \\left( {\\cos t} \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{{{\\cos }^2}t &#8211; {{\\operatorname{sen} }^2}t}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{i'(z)}&amp; = &amp;{{{\\left( {3z\\cos z} \\right)}^\\prime }} \\\\<br \/>\n{}&amp; = &amp;{{{\\left( {3z} \\right)}^\\prime } \\times \\cos z + 3z \\times {{\\left( {\\cos z} \\right)}^\\prime }} \\\\<br \/>\n{}&amp; = &amp;{3\\cos z &#8211; 3z\\operatorname{sen} z}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{j'(x)}&amp; = &amp;{\\left( {3x\\operatorname{tg} x} \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{\\left( {3x} \\right)&#8217; \\times \\operatorname{tg} x + 3x \\times \\left( {\\operatorname{tg} x} \\right)&#8217;} \\\\<br \/>\n{}&amp; = &amp;{\\begin{array}{*{20}{c}}<br \/>\n{3\\operatorname{tg} x + \\frac{{3x}}{{{{\\cos }^2}x}},}&amp;{x \\ne \\frac{\\pi }{2} + k\\pi ,k \\in \\mathbb{Z}}<br \/>\n\\end{array}}<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8651' onClick='GTTabs_show(0,8651)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcule a derivada de cada uma das fun\u00e7\u00f5es reais de vari\u00e1vel real: $f:x \\to 3 + 2\\cos x$ $g:x \\to \\operatorname{sen} x + \\cos x$ $h:t \\to \\operatorname{sen} t.\\cos t$ $i:z&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19672,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,295],"tags":[427,293,307],"series":[],"class_list":["post-8651","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-seno-co-seno-e-tangente","tag-12-o-ano","tag-funcao-derivada","tag-funcoes-trigonometricas"],"views":1968,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8651","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=8651"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8651\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19672"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8651"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8651"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8651"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8651"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}