{"id":668,"date":"2016-09-06T15:41:53","date_gmt":"2016-09-06T15:41:53","guid":{"rendered":"http:\/\/wordpress.rose-hulman.edu\/rickert\/?page_id=668"},"modified":"2017-03-27T15:47:07","modified_gmt":"2017-03-27T15:47:07","slug":"ma111-basic-skills-summary","status":"publish","type":"page","link":"https:\/\/wordpress.rose-hulman.edu\/rickert\/ma111-basic-skills-summary\/","title":{"rendered":"MA111 &#8220;Basic Skills&#8221; Summary"},"content":{"rendered":"<p>Please <a href=\"mailto:john.rickert@rose-hulman.edu\"><u>e-mail me<\/u><\/a> if you have any useful suggestions about this page.<\/p>\n<p>You should know the definition of the derivative<\/p>\n<p>Know The <strong>Power Rule<\/strong>: ( <em>x<sup>n<\/sup><\/em> )&#8217; = <em>n x<sup>n-1<\/sup><\/em><\/p>\n<p>( sin(<em>x<\/em>) )&#8217; = cos(<em>x<\/em>)<\/p>\n<p>( cos(<em>x<\/em>) )&#8217; = -sin(<em>x<\/em>)<\/p>\n<p>( tan(<em>x<\/em>) )&#8217; = sec<sup>2<\/sup>(<em>x<\/em>)<\/p>\n<p>( cot(<em>x<\/em>) )&#8217; = -csc<sup>2<\/sup>(<em>x<\/em>)<\/p>\n<p>( sec(<em>x<\/em>) )&#8217; = sec(<em>x<\/em>) tan(<em>x<\/em>)<\/p>\n<p>( csc(<em>x<\/em>) )&#8217; = -csc(<em>x<\/em>) cot(<em>x<\/em>)<\/p>\n<p>&nbsp;<\/p>\n<p>( arcsin(<em>x<\/em>) )&#8217; = 1\/sqrt(1-<em>x<\/em><sup>2<\/sup>)<\/p>\n<p>( arccos(<em>x<\/em>) )&#8217; = -1\/sqrt(1-<em>x<\/em><sup>2<\/sup>)<\/p>\n<p>( arctan(<em>x<\/em>) )&#8217; = 1\/(1+<em>x<\/em><sup>2<\/sup>)<\/p>\n<p>( arccot(<em>x<\/em>) )&#8217; = -1\/(1+<em>x<\/em><sup>2<\/sup>)<\/p>\n<p>( arcsec(<em>x<\/em>) )&#8217; = 1\/sqrt(<em>x<\/em><sup>2<\/sup>-1)<\/p>\n<p>( arccsc(<em>x<\/em>) )&#8217; = -1\/sqrt(<em>x<\/em><sup>2<\/sup>-1)<\/p>\n<p>&nbsp;<\/p>\n<p>( sinh(<em>x<\/em>) )&#8217; = cosh(<em>x<\/em>)<\/p>\n<p>( cosh(<em>x<\/em>) )&#8217; = sinh(<em>x<\/em>)<\/p>\n<p>&nbsp;<\/p>\n<p>( e<em><sup>x<\/sup><\/em> ) &#8216; = e<em><sup>x<\/sup><\/em><\/p>\n<p>( ln(<em>x<\/em>) )&#8217; = 1\/<em>x<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>The <strong>Product Rule<\/strong>: (f*g)&#8217; = f&#8217;*g + f*g&#8217;<\/p>\n<p>The <strong>Quotient Rule<\/strong>: ( f \/ g )&#8217; = (g*f&#8217; &#8211; f*g&#8217;) \/ g<sup>2<\/sup><\/p>\n<p>The <strong>Chain Rule<\/strong>: ( f(g(x)) ) &#8216; = f'(g(x)) * g'(x)<\/p>\n<p><strong>Implicit Differentiation<\/strong><\/p>\n<hr \/>\n<p>Some good elementary practice exercises from Thomas&#8217; <em>Calculus:Early Transcendental Functions<\/em>, 11th ed.<\/p>\n<p>Section 3.1 #27-43<\/p>\n<p>Section 3.2 #1-46<\/p>\n<p>Section 3.3 #1-30<\/p>\n<p>Section 3.4 #1-46<\/p>\n<p>Section 3.5 #1-108<\/p>\n<p>Section 3.6 #1-66<\/p>\n<p>Section 3.7 #1-96<\/p>\n<p>Section 3.8 #49-74<\/p>\n<p>Section 3.10 #1-66<\/p>\n<p>Other exercises in these sections are good for providing deeper insight into the derivative.<\/p>\n<hr \/>\n<p>Go to<\/p>\n<ul>\n<li>Dr. Rickert&#8217;s <a href=\"http:\/\/wordpress.rose-hulman.edu\/rickert\/ma111-calculus-i\/\" target=\"_blank\"><u>MA111 page<\/u><\/a><\/li>\n<li>the <a href=\"http:\/\/www.rose-hulman.edu\/academics\/academic-departments\/mathematics.aspx\" target=\"_blank\"><u>Mathematics Department Home Page <\/u><\/a><\/li>\n<li>Dr. Rickert&#8217;s <a href=\"http:\/\/www.rose-hulman.edu\/~rickert\/Classes\"><u>classes page<\/u><\/a><\/li>\n<li>Dr. Rickert&#8217;s <a href=\"http:\/\/wordpress.rose-hulman.edu\/rickert\/\" target=\"_blank\"><u>home page<\/u><\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p class=\"excerpt\">Please e-mail me if you have any useful suggestions about this page. You should know the definition of the derivative Know The Power Rule: ( xn )&#8217; = n xn-1 ( sin(x) )&#8217; = cos(x) ( cos(x) )&#8217; = -sin(x) ( tan(x) )&#8217; = sec2(x) ( cot(x) )&#8217; = -csc2(x) ( sec(x) )&#8217; = sec(x) tan(x) ( csc(x) )&#8217; =&hellip;<\/p>\n<p class=\"more-link-p\"><a class=\"btn btn-default\" href=\"https:\/\/wordpress.rose-hulman.edu\/rickert\/ma111-basic-skills-summary\/\">Read more<\/a><\/p>\n","protected":false},"author":812,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-668","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/wordpress.rose-hulman.edu\/rickert\/wp-json\/wp\/v2\/pages\/668","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wordpress.rose-hulman.edu\/rickert\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wordpress.rose-hulman.edu\/rickert\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wordpress.rose-hulman.edu\/rickert\/wp-json\/wp\/v2\/users\/812"}],"replies":[{"embeddable":true,"href":"https:\/\/wordpress.rose-hulman.edu\/rickert\/wp-json\/wp\/v2\/comments?post=668"}],"version-history":[{"count":4,"href":"https:\/\/wordpress.rose-hulman.edu\/rickert\/wp-json\/wp\/v2\/pages\/668\/revisions"}],"predecessor-version":[{"id":3611,"href":"https:\/\/wordpress.rose-hulman.edu\/rickert\/wp-json\/wp\/v2\/pages\/668\/revisions\/3611"}],"wp:attachment":[{"href":"https:\/\/wordpress.rose-hulman.edu\/rickert\/wp-json\/wp\/v2\/media?parent=668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}