The derivative of a logarithm (be it natural or base-10) ##ln[f(x)]## is given by the formula:<\/p>\n
f'(x) \/ f(x)<\/p>\n
Where f'(x) is the derivative of the original function f(x).<\/p>\n
Ok, keep that aside for a while.<\/p>\n
Now, going back to logarithms properties, we have that ##ln(x)^m## = ##m.ln(x)##<\/p>\n
Then, we have in your example:<\/p>\n
##ln(x)^ln(x)## = ##ln(x)## . ##ln(x)##<\/p>\n
Deriving it consists on deriving a product, which consists on:<\/p>\n
Derivative of the first function times the original second function PLUS Derivative of the second function times the original first function<\/p>\n
Like this:<\/p>\n
##1\/x . ln(x)## + ##ln(x) + 1\/x## = ##2.ln(x)\/x##<\/p>\n
\ud83d\ude42<\/p>\n","protected":false},"excerpt":{"rendered":"
The derivative of a logarithm (be it natural or base-10) ##ln[f(x)]## is given by the formula: f'(x) \/ f(x) Where f'(x) is the derivative of the original function f(x). Ok, keep that aside for a while. Now, going back to Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-71942","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/71942","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=71942"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/71942\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=71942"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=71942"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=71942"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}