[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-315347-105":59,"doc-detail-315347-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","w5-vce-2019-mm-year-12-calc-diffn-mixed-worksheet-2-calculus-practice-problems","W5-VCE-2019-MM-Year-12-Calc-Diffn-MIXED-Worksheet-2 - Calculus Practice Problems","","This document serves as a comprehensive practice worksheet for VCE Mathematical Methods students, specifically focusing on the topic of differentiation in Year 12. It contains a diverse set of thirteen mathematical functions, labeled (a) through (m), that require students to calculate their derivatives with respect to x. These problems encompass a variety of mathematical operations, including trigonometric, logarithmic, exponential, and power functions, as well as complex expressions involving products and quotient rules. Additionally, the document provides a step-by-step worked solution for the specific function f(x) = e^x(loge x)^2, demonstrating the correct application of the product rule and chain rule to arrive at the final derivative result. This material is designed to reinforce calculus proficiency through structured repetition and analytical practice.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/w5-vce-2019-mm-year-12-calc-diffn-mixed-worksheet-2-calculus-practice-problems/315347/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/w5-vce-2019-mm-year-12-calc-diffn-mixed-worksheet-2-calculus-practice-problems/315347.png","ImageObject",300,407,{"name":92,"@type":93},"Violet","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the primary objective of this worksheet?","Question",{"text":113,"@type":114},"The primary objective is to practice finding the derivative of various mathematical functions with respect to x.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What mathematical concepts are covered in the problems?",{"text":118,"@type":114},"The problems cover a range of concepts including trigonometric functions, logarithms, exponential functions, and the application of product and chain rules for differentiation.",{"name":120,"@type":111,"acceptedAnswer":121},"Does the document provide solutions to all problems?",{"text":122,"@type":114},"No, it provides a comprehensive list of practice problems and a detailed step-by-step worked solution for one specific function: f(x) = e^x(loge x)^2.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},315347,1789904564,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144,"preview_page_count":4},4398048950312,"https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908","Differentiate the following equations with respect to x .  \n(a) f (x) 􀀠 2sin 􀀋3x􀀌cos􀀋4x􀀌  \n(b) f (x) 􀀠 1􀀎 ln x 2􀀎 3ex  \n(c) f (x) 􀀠 xcosx  \n(d) f (x) 􀀠 􀀋 xex 􀀌􀁓  \n 1   \n(e) f (x) 􀀠 x0.4  \n􀂧 􀁓􀂷(f) f (x) 􀀠 tan 􀂨􀂩 2􀁓x􀀎 2 􀂹􀂸  \n 1   \n(g) f (x) 􀀠 􀀋 3x4 􀀎 x􀀐 8􀀌9  \n(h) f (x) 􀀠 ex 􀀋loge x􀀌2  \n(i) f (x) 􀀠 􀀋 x4 􀀎 x􀀌􀀋2x􀀐1􀀌  \n(j) f (x) 􀀠 3ex 􀀐 7loge x  \n(k) f (x) 􀀠 􀀋2x􀀐1􀀌3 􀀋 x2 􀀐3􀀌2  \n(l) f (x) 􀀠 x sin x􀀎 cos x  \n(m) f (x) 􀀠 2x3􀀐~~ ~~xx  \n(a) f (x) 􀀠 2sin 􀀋3x􀀌cos􀀋4x􀀌  \n(b) f (x) 􀀠 1􀀎 ln x 2􀀎 3ex  \n(c) f (x) 􀀠 xcosx  \n(d) f (x) 􀀠 􀀋 xex 􀀌􀁓  \n1 (e) f (x) 􀀠 x0.4  \n􀂧  \n(f) f (x) 􀀠 tan 􀂨􀂩 2􀁓x􀀎  \n􀁓􀂷  \n2 􀂹􀂸  \n(g) f (x) 􀀠  1   \n􀀋 3x4 􀀎 x􀀐8􀀌9  \n(h) f (x) 􀀠 ex 􀀋loge x􀀌2  \n(i) f (x) 􀀠 􀀋 x4 􀀎 x􀀌􀀋2x􀀐1􀀌  \n(j) f (x) 􀀠 3ex 􀀐 7loge x  \n(k) f (x) 􀀠 􀀋2x􀀐1􀀌3 􀀋 x2 􀀐3􀀌2  \n(l) f (x) 􀀠 x sin x􀀎 cos x  \n(m) f (x) 􀀠 2x3􀀐~~ ~~xx","cbCaiijsWj81rmsF","https://ap.wps.com/l/cbCaiijsWj81rmsF","pdf",582428,"English","# Differentiation Practice Problems\n## Problem Set\n## Worked Solution Analysis","[{\"question\":\"What is the primary objective of this worksheet?\",\"answer\":\"The primary objective is to practice finding the derivative of various mathematical functions with respect to x.\"},{\"question\":\"What mathematical concepts are covered in the problems?\",\"answer\":\"The problems cover a range of concepts including trigonometric functions, logarithms, exponential functions, and the application of product and chain rules for differentiation.\"},{\"question\":\"Does the document provide solutions to all problems?\",\"answer\":\"No, it provides a comprehensive list of practice problems and a detailed step-by-step worked solution for one specific function: f(x) = e^x(loge x)^2.\"}]","W5-VCE-2019-MM-Year-12-Calc-Diffn-MIXED-Worksheet-2 - Calculus Practice Problems | PDF",25]