[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571481-105":53,"doc-detail-571481-en":127},{"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":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","derivatives-cheat-sheet","Derivatives Cheat Sheet","","This document serves as a concise and comprehensive reference guide for essential calculus derivative rules. It outlines fundamental operations including the Constant Rule, Power Rule, Product Rule, Quotient Rule, and the Chain Rule. Additionally, it provides specific derivative formulas for exponential and logarithmic functions, including natural logarithmic derivatives. The guide further extends these principles by providing generalized chain rule applications for composite functions, such as power-based chains, exponential chains with base a, natural exponential chains, and logarithmic chains. It is designed for students and professionals seeking a quick, reliable summary for solving differential equations and calculus problems efficiently. The layout facilitates rapid lookup of complex derivation procedures, ensuring accurate implementation of mathematical principles in academic or analytical settings.",{"@graph":63,"@context":119},[64,80,102],{"@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":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/derivatives-cheat-sheet/571481/",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/derivatives-cheat-sheet/571481.png","ImageObject",442,249,{"name":88,"@type":89},"404brain","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-23","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",8,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What is the Power Rule for derivatives?","Question",{"text":109,"@type":110},"The Power Rule states that the derivative of x^n with respect to x is equal to nx^(n-1).","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"How is the derivative of a natural exponential function calculated?",{"text":114,"@type":110},"The derivative of e^x with respect to x remains e^x.",{"name":116,"@type":107,"acceptedAnswer":117},"What is the purpose of the Chain Rule in this guide?",{"text":118,"@type":110},"The Chain Rule is provided as a method to find the derivative of composite functions, with several generalized examples shown for power, exponential, and logarithmic functions.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},571481,1792002596,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":9,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":4},1099529839291,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Derivatives Cheat Sheet  \nDerivative Rules  \n1. Constant Rule: ddx (c) = 0 ; where c is a constant  \n2. Power Rule: ddx (xn ) = nxn􀀀1  \n3. Product Rule: (fg)0 = f 0g + fg0  \n4. Quotient Rule: 􀀒 fg 􀀓 0 = f~~ ~~0g~~ ~~~~ ~~fg0  \n5. Chain Rule: (f(g(x))0 = f0 (g(x))g0 (x)  \nExponential & Logarithmic Functions  \nddx (ax ) = ax ln(a) ~~ ~~ddx (ex ) = ex  \n d   1   d   1  \ndx (loga (x)) = x ln(a) dx (ln(x)) = x  \nChain Rule  \nThese rules are all generalizations of the above rules using the chain rule.  \n1. ddx ([g(x)]n ) = n[g(x)]n􀀀1g0 (x)  \n2. ddx (ag (x)) = ag (x)g0 (x) ln(a)  \n3. ddx (eg (x)) = eg (x)g0 (x)  \n4. ddx (loga jg(x)j) = g~~ ~~(x)1ln(a)g0 (x)  \n5. ddx (ln jg(x)j) = g~~ ~~1(x) g0 (x)","cbCaifKsSkXlZ40e","https://ap.wps.com/l/cbCaifKsSkXlZ40e","pdf",98617,"English","# Derivative Rules\n## Exponential and Logarithmic Functions\n## Chain Rule Generalizations","[{\"question\":\"What is the Power Rule for derivatives?\",\"answer\":\"The Power Rule states that the derivative of x^n with respect to x is equal to nx^(n-1).\"},{\"question\":\"How is the derivative of a natural exponential function calculated?\",\"answer\":\"The derivative of e^x with respect to x remains e^x.\"},{\"question\":\"What is the purpose of the Chain Rule in this guide?\",\"answer\":\"The Chain Rule is provided as a method to find the derivative of composite functions, with several generalized examples shown for power, exponential, and logarithmic functions.\"}]","Derivatives Cheat Sheet | PDF",1791919927]