[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522836-105":59,"doc-detail-522836-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","logarithmic-differentiation-use-logarithmic-differentiation-to-differentiate-each-function-with-respect-to-x","Logarithmic Differentiation - Use logarithmic differentiation to differentiate each function with respect to x","","Worksheets for Infinite Calculus practice on logarithmic differentiation. The document instructs students to use logarithmic differentiation to differentiate each given function with respect to x, without needing to simplify or substitute for y. It presents multiple problems of the form y expressed using powers of x and polynomial expressions, followed by space for answers, including derivative expressions computed from ln-based differentiation rules.",{"@graph":69,"@context":122},[70,84,105],{"@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/logarithmic-differentiation-use-logarithmic-differentiation-to-differentiate-each-function-with-respect-to-x/522836/",{"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/logarithmic-differentiation-use-logarithmic-differentiation-to-differentiate-each-function-with-respect-to-x/522836.png","ImageObject",300,407,{"name":92,"@type":93},"Jordan Avery","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-12","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main method used in these problems?","Question",{"text":112,"@type":113},"The worksheet uses logarithmic differentiation to differentiate each function with respect to x.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Do students need to simplify the final answers?",{"text":117,"@type":113},"No. The instruction states that simplification or substitution for y is not needed.",{"name":119,"@type":110,"acceptedAnswer":120},"What kinds of functions are included?",{"text":121,"@type":113},"The problems use expressions involving powers of x and polynomial factors, typically written as products and powers inside logarithmic differentiation.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522836,1791513029,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52},1099523882367,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Kuta Software-Infinite Calculus Name   \nLogarithmic Differentiation Date  Period   \nUse logarithmic differentiation to differentiate each function with respect to x.  \n1) y = 2x2x 2) y = 5x5x  \n3x x4  \n3) y = 3x 4) y = 4x  \n5) y = (3x4 + 4) 3 5x3 + 1 6) y = (x5 + 5)2 2x2 + 3  \n(3x4 − 2) 5  8) y = 3x2 + 1 (3x4 + 1) 3  \n7) y =  \n(3x3 + 4) 2  \n2x3 + 3 10) y = (2x2 − 5) 3 x 2 − 2  \n9) y = ~~ ~~  \n(x4 − 3) 3  \nUse logarithmic differentiation to differentiate each function with respect to x. You do not need to simplify or substitute for y.  \n(5x − 4) 4 12) y = (x + 2)4 ⋅ (2x − 5)2 ⋅ (5x + 1) 3  \n11) y = ~~ ~~  \n(3x2 + 5) 5 ⋅ (5x4 − 3) 3  \n13) y = (5x5 + 2)2 ⋅ (3x3 − 1) 3 ⋅ (3x − 1)4  (x2 + 3) 4   \n14) y =  \n(5x5 − 2) 5 ⋅ (3x2 − 5)2  \n15) y = (3x3 − 4) 5 ⋅ (3x − 1) 3 ⋅ (5x3 − 2)2 ⋅ ( x + 3) 4  \n (4x2 − 5)2   \n16) y =  \n(2x − 3) 4 ⋅ (5x4 − 2) 5 ⋅ (3x2 − 4) 3  \nKuta Software-Infinite Calculus Name   \nLogarithmic Differentiation Date  Period   \nUse logarithmic differentiation to differentiate each function with respect to x.  \n1) y = 2x2x  \ndydx = y(2 ln x + 2)  \n= 4x2x(ln x + 1)  \n3) y = 3x3x  \ndydx = y(3 ln x + 3)  \n= 9x3x(ln x + 1)  \n5) y = (3x4 + 4) 3 5x3 + 1  \ndydx = y(~~ ~~336x44~~ ~~ + ~~ ~~1510x3x~~ ~~2~~ ~~)  \n3x2 (3x4 + 4) 2 ( 135x4 + 24x + 20) =  \n2 5x3 + 1  \n(3x4 − 2) 5  \n7) y = ~~ ~~  \n(3x3 + 4) 2  \ndydx = y(~~ ~~360x42~~ ~~ − 318x34~~ ~~)  \n6x2 (3x4 − 2) 4 (21x4 + 40x + 6) =  \n(3x3 + 4) 3  \n2) y = 5x5x  \ndydx = y(5 ln x + 5)  \n= 25x5x(ln x + 1)  \n4) y = 4xx4  \ndydx = y(4x3 ln x + x3 )= 4xx4 + 3 (4 ln x + 1)  \n6) y = (x5 + 5)2 2x2 + 3  \ndydx = y(~~ ~~1x5045~~ ~~ + ~~ ~~2x22~~ ~~3~~ ~~)   \n2x(x5 + 5)( 11x5 + 15x3 + 5)=  \n2x2 + 3  \n8) y = 3x2 + 1 (3x4 + 1) 3  \ndydx = y(~~ ~~3x32~~ ~~1~~ ~~ + ~~ ~~336x4~~ ~~1~~ ~~)  \n3x(3x4 + 1) 2 (39x4 + 1 + 12x2 ) =  \n3x2 + 1  \n2x3 + 3  \n9) y = ~~ ~~  \n(x4 − 3) 3  \ndydx = y(~~ ~~23x3x~~ ~~3~~ ~~ − 1x4233~~ ~~)  \n3x2 (−7x4 − 3 − 12x)=  \n(x4 − 3) 4 2x3 + 3  \n10) y = (2x2 − 5) 3 x 2 − 2  \ndydx = y(~~ ~~21x22~~ ~~5~~ ~~ + ~~ ~~x2~~ ~~~~ ~~2~~ ~~) x(2x2 − 5) 2 ( 14x2 − 29)   \n=  \nx 2 − 2  \nUse logarithmic differentiation to differentiate each function with respect to x. You do not need to simplify or substitute for y.  \n(5x − 4) 4 12) y = (x + 2)4 ⋅ (2x − 5)2 ⋅ (5x + 1) 3  \n11) y = ~~ ~~  \ndy (3x2 +520) 5 ⋅ (5x4 −303x) 3 60x3 ~~ ~~dydx = y(~~ ~~x~~ ~~~~ ~~2 + ~~ ~~2x~~ ~~5~~ ~~ + ~~ ~~5x1~~ ~~1~~ ~~ )  \ndx = y( 5x − 4 − 3x2 + 5  − 5x4 − 3 )  \n13) y = (5x5 + 2)2 ⋅ (3x3 − 1) 3 ⋅ (3x − 1)4 (x2 + 3) 4  \n14) y = ~~ ~~  \ndydx = y(~~ ~~550x52~~ ~~ + ~~ ~~327x3~~ ~~1~~ ~~ + ~~ ~~3x1~~ ~~1~~ ~~ ) dy (5x5 − 2) 5 ⋅ (3x2 − 5  \ndx = y(~~ ~~x28~~ ~~3~~ ~~ − 512x55~~ ~~2~~ ~~ − 31x22~~ ~~5~~ ~~)  \n15) y = (3x3 − 4) 5 ⋅ (3x − 1) 3 ⋅ (5x3 − 2)2 ⋅ ( x + 3) 4  \ndydx = y(~~ ~~345x34~~ ~~ + ~~ ~~3x~~ ~~1~~ ~~ + ~~ ~~530x32~~ ~~ + ~~ ~~x~~ ~~~~ ~~3~~ ~~ )  \n(4x2 − 5)2  \n16) y = ~~ ~~  \n(2x − 3) 4 ⋅ (5x4 − 2) 5 ⋅ (3x2 − 4) 3  \ndydx = y(~~ ~~41x26~~ ~~5~~ ~~ − 2x~~ ~~3~~ ~~ − 510x4032~~ ~~ − 31x28~~ ~~4~~ ~~)  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaihqFBH39NZCI","https://ap.wps.com/l/cbCaihqFBH39NZCI","pdf",42217,"English","# Logarithmic Differentiation Practice\n## Instructions\n## Differentiation Problems","[{\"question\":\"What is the main method used in these problems?\",\"answer\":\"The worksheet uses logarithmic differentiation to differentiate each function with respect to x.\"},{\"question\":\"Do students need to simplify the final answers?\",\"answer\":\"No. The instruction states that simplification or substitution for y is not needed.\"},{\"question\":\"What kinds of functions are included?\",\"answer\":\"The problems use expressions involving powers of x and polynomial factors, typically written as products and powers inside logarithmic differentiation.\"}]","Logarithmic Differentiation - Use logarithmic differentiation to differentiate each function with respect to x | PDF",1791426220]