[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571485-105":53,"doc-detail-571485-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","derivative-rules","Derivative Rules","","Derivative Rules summarizes core results for differentiating common functions. It presents the Constant Rule, Constant Multiple Rule, Power Rule, Sum and Difference Rule, Product Rule, Quotient Rule, and Chain Rule. It also lists derivatives for trigonometric functions (sin, cos, tan, sec, cot, csc), along with exponential forms (a^x, e^x, a^{g(x)}, e^{g(x)}) and logarithmic forms (log_a(x), ln(x), log_a(g(x)), and ln(g(x))).",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/derivative-rules/571485/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/derivative-rules/571485.png","ImageObject",442,249,{"name":88,"@type":89},"lilac","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-20","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":47},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What is the Constant Rule for derivatives?","Question",{"text":108,"@type":109},"If f(x)=c, then the derivative f'(x)=0.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How do you differentiate a product of functions?",{"text":113,"@type":109},"For h(x)=f(x)g(x), use the Product Rule: h'(x)=f'(x)g(x)+f(x)g'(x).",{"name":115,"@type":106,"acceptedAnswer":116},"What is the Chain Rule?",{"text":117,"@type":109},"For h(x)=f(g(x)), the derivative is h'(x)=f'(g(x))g'(x).","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},571485,1792033668,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":47,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":9,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":4},3985747861865,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","List of Derivative Rules  \nBelow is a list of all the derivative rules we went over in class.  \n􀀏 Constant Rule: f (x) = c then f0 (x) = 0  \n􀀏 Constant Multiple Rule: g (x) = c 􀀁 f(x) then g 0 (x) = c 􀀁 f0 (x)  \n􀀏 Power Rule: f (x) = xn then f0 (x) = nxn􀀀1  \n􀀏 Sum and Di􀀋erence Rule: h (x) = f(x)􀀆g(x) then h0 (x) = f 0 (x)􀀆g0 (x)  \n􀀏 Product Rule: h (x) = f (x)g (x) then h0 (x) = f0 (x)g (x) + f(x)g 0 (x)  \nf (x) 0  f 0 (x)g (x) 􀀀 f(x)g 0 (x)  \n􀀏 Quotient Rule: h (x) = then h (x) =  \ng (x) g (x)2  \n􀀏 Chain Rule: h (x) = f (g(x)) then h0 (x) = f0 (g(x))g0 (x)  \n􀀏 Trig Derivatives:  \n– f (x) = sin(x) then f 0 (x) = cos(x)  \n– f (x) = cos(x) then f 0 (x) = 􀀀 sin(x)  \n– f (x) = tan(x) then f 0 (x) = sec2 (x)  \n– f (x) = sec(x) then f 0 (x) = sec(x) tan(x)  \n– f (x) = cot(x) then f 0 (x) = 􀀀 csc2 (x)  \n– f (x) = csc(x) then f 0 (x) = 􀀀 csc(x) cot(x)  \n􀀏 Exponential Derivatives  \n– f (x) = ax then f0 (x) = ln(a)ax  \n– f (x) = ex then f0 (x) = ex  \n– f (x) = ag (x) then f0 (x) = ln(a)ag (x)g 0 (x)  \n– f (x) = eg (x) then f0 (x) = eg (x)g 0 (x)  \n􀀏 Logarithm Derivatives  \n– f (x) = loga (x) then f 0 (x) = ln(1a)x –  1  \nf (x) = ln(x) then f 0 (x) =  \nx  \n– f (x) = loga (g(x)) then f 0 (x) = ln~~ ~~g(a0~~ ~~)(xg)(x)  \n–  g 0 (x) f (x) = ln(g(x)) then f 0 (x) =  \ng (x)","cbCaikXF2HKfL7mo","https://ap.wps.com/l/cbCaikXF2HKfL7mo","pdf",22445,"English","# Derivative Rules\n## Basic Differentiation Rules\n## Trigonometric Derivatives\n## Exponential Derivatives\n## Logarithm Derivatives","[{\"question\":\"What is the Constant Rule for derivatives?\",\"answer\":\"If f(x)=c, then the derivative f'(x)=0.\"},{\"question\":\"How do you differentiate a product of functions?\",\"answer\":\"For h(x)=f(x)g(x), use the Product Rule: h'(x)=f'(x)g(x)+f(x)g'(x).\"},{\"question\":\"What is the Chain Rule?\",\"answer\":\"For h(x)=f(g(x)), the derivative is h'(x)=f'(g(x))g'(x).\"}]","Derivative Rules | PDF",1791919971]