[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522819-105":59,"doc-detail-522819-en":123},{"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":116,"head_meta":118,"extra_data":120,"updated_unix":122},105,"en","differentiation-logs-and-exponentials-chain-rule-with-logs-exponentials-practice","Differentiation - Logs and Exponentials - Chain Rule with Logs, Exponentials Practice","","Differentiation worksheet focused on differentiating functions with respect to x, emphasizing logarithmic and exponential forms. Problems apply the chain rule across multiple examples involving powers, logarithms, and trigonometric components, producing derivative expressions that include natural-log factors such as ln 4, ln 2, ln 3, and ln 5. The sheet also includes worked solution steps showing intermediate algebraic rearrangements and final simplified derivatives for each item.",{"@graph":69,"@context":115},[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/differentiation-logs-and-exponentials-chain-rule-with-logs-exponentials-practice/522819/",{"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/differentiation-logs-and-exponentials-chain-rule-with-logs-exponentials-practice/522819.png","ImageObject",300,407,{"name":92,"@type":93},"Riley West","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109],{"name":110,"@type":111,"acceptedAnswer":112},"What does the chain rule contribute to the solutions?","Question",{"text":113,"@type":114},"For each composite inside expression, the worksheet multiplies the outside derivative by the derivative of the inside, producing factors like powers of x and inside polynomial coefficients in the final simplified form.","Answer","https://schema.org",{"og:url":83,"og:type":117,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":119,"canonical":83},"index,follow",{"doc_id":121,"site_id":62},522819,1791488674,{"code":4,"msg":5,"data":124},{"doc_id":121,"user_id":125,"nickname":92,"user_avatar":126,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":127,"file_id":128,"file_url":129,"file_type":130,"file_size":131,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":132,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":133,"faqs":134,"seo_title":135,"seo_description":67,"update_tm":136,"read_time":24,"preview_page_count":4},1099523885074,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Kuta Software-Infinite Calculus Name   \nDifferentiation-Logs and Exponentials Date  Period   \nDifferentiate each function with respect to x.  \n4x4 −5x3  \n1) y = 4 2) y = 4  \n3) y = log 3 3x2 4) y = log 2 4x2  \n5) y = log 3 (3x5 + 5) 5 6) y = log 5 (−5x3 − 2) 3  \n7) y = (4 x3 + 2) 3 8) y = 3 ( x4 + 1)3  \n9) y = 3 cos 3x4 10) y = log 5 tan 4x4  \nKuta Software-Infinite Calculus Name   \nDifferentiation-Logs and Exponentials Date  Period   \nDifferentiate each function with respect to x.  \n1) y = 44x4  \ndydx = 44x4 ln 4 ⋅ 16x3  \n3 4x4 + 2 = x ⋅ 4 ln 4  \n3) y = log 3 3x2  \ndy 1  \n~~ ~~ =  2  ⋅ 6x  \ndx 3x ln 3  \n2  \n= ~~ ~~  \nx ln 3  \n5) y = log 3 (3x5 + 5) 5  \ndydx = ~~ ~~(3x5~~ ~~+~~ ~~15)~~ ~~5~~ ~~ln~~ ~~3 ⋅ 5(3x5 + 5)4 ⋅ 15x4  75x4   \n=  \nln 3 ⋅ (3x5 + 5)  \n7) y = (4 x3 + 2) 3  \ndydx = 3(4 x3 + 2) 2 ⋅ 4 x3 ln 4 ⋅ 3x2 = 9x2 (4 x3 + 2)2 ⋅ 4 x3 ln 4  \n9) y = 3 cos 3x4  \ndydx = 3 cos 3x4 ln 3 ⋅ −1sin 3x4 ⋅ 12x3 = −4x3 ⋅ 3 cos 3x4 + 1 sin 3x4 ⋅ ln 3  \n2) y = 4 −5x3  \ndydx = 4 −5x3 ln 4 ⋅ −15x2  \n 15x2 ln 4 = −  \n45x3  \n4) y = log 2 4x2  \ndy 1  \n~~ ~~ =  2  ⋅ 8x  \ndx 4x ln 2  \n2  \n= ~~ ~~  \nx ln 2  \n6) y = log 5 (−5x3 − 2) 3  \ndydx = ~~ ~~(−5x3~~ ~~−12)~~ ~~3~~ ~~ln~~ ~~5 ⋅ 3(−5x3 − 2) 2 ⋅ −15x2  45x2   \n= −  \nln 5 ⋅ (−5x3 − 2)  \n8) y = 3 ( x4 + 1)3  \ndydx = 3 ( x4 + 1)3 ln 3 ⋅ 3( x4 + 1)2 ⋅ 4x3 = 4x3 ⋅ 3 ( x4 + 1)3 + 1 ⋅ (x4 + 1) 2 ln 3  \n10) y = log 5 tan 4x4  \ndydx = tan~~ ~~4x14~~ ~~⋅~~ ~~ln~~ ~~5 ⋅ sec 2 4x4 ⋅ 16x3  \n 16x3 ⋅ sec 2 4x4   \n=  \ntan 4x4 ⋅ ln 5  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiv6ZHKfQwPaB","https://ap.wps.com/l/cbCaiv6ZHKfQwPaB","pdf",28117,"English","# Differentiate each function with respect to x\n## Logarithmic functions and chain rule\n## Exponential expressions and derivatives","[{\"question\":\"What does the chain rule contribute to the solutions?\",\"answer\":\"For each composite inside expression, the worksheet multiplies the outside derivative by the derivative of the inside, producing factors like powers of x and inside polynomial coefficients in the final simplified form.\"}]","Differentiation - Logs and Exponentials - Chain Rule with Logs, Exponentials Practice | PDF",1791426203]