{"id":539965,"date":"2023-04-23T01:33:32","date_gmt":"2023-04-22T20:03:32","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/for-a-differentiable-function-define-d%e2%88%97fxlimh%e2%86%920%e2%81%a1f2xh%e2%88%92f2xh-where-f2xfx2-for-example-d%e2%88%97fx2x-if-fxx-2\/"},"modified":"2025-06-20T13:27:39","modified_gmt":"2025-06-20T07:57:39","slug":"for-a-differentiable-function-define-d%e2%88%97fxlimh%e2%86%920%e2%81%a1f2xh%e2%88%92f2xh-where-f2xfx2-for-example-d%e2%88%97fx2x-if-fxx-2","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/for-a-differentiable-function-definedfxlimh0f2xh\/","title":{"rendered":"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex","custom_permalink":"question\/mathematics\/for-a-differentiable-function-definedfxlimh0f2xh\/"},"categories":[],"acf":{"question":"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex","options":null,"solution":"<p>For a differentiable function, define \\( D&lowast;f(x) = \\lim_{h \\to 0} \\frac{f^2(x+h) - f^2(x)}{h} \\) where \\( f^2(x) = (f(x))^2 \\).<\/p>\r\n<p>For example:<\/p>\r\n<ul>\r\n<li>\\( D&lowast;f(x) = 2x \\) if \\( f(x) = x \\)<\/li>\r\n<li>\\( D&lowast;f(x) = 2 \\sin(x) \\cos(x) \\) if \\( f(x) = \\sin(x) \\)<\/li>\r\n<li>\\( D&lowast;f(x) = 2 e^{2x} \\) if \\( f(x) = e^x \\)<\/li>\r\n<\/ul>","subject":"Mathematics"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/for-a-differentiable-function-definedfxlimh0f2xh\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/for-a-differentiable-function-definedfxlimh0f2xh\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-20T07:57:39+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex - Infinity Learn by Sri Chaitanya","description":"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/for-a-differentiable-function-definedfxlimh0f2xh\/","og_locale":"en_US","og_type":"article","og_title":"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex - Infinity Learn by Sri Chaitanya","og_description":"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex","og_url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/for-a-differentiable-function-definedfxlimh0f2xh\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_modified_time":"2025-06-20T07:57:39+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@InfinityLearn_","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/for-a-differentiable-function-definedfxlimh0f2xh\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/for-a-differentiable-function-definedfxlimh0f2xh\/","name":"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2023-04-22T20:03:32+00:00","dateModified":"2025-06-20T07:57:39+00:00","description":"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/for-a-differentiable-function-definedfxlimh0f2xh\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/question\/mathematics\/for-a-differentiable-function-definedfxlimh0f2xh\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/for-a-differentiable-function-definedfxlimh0f2xh\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"For a differentiable function, define\u00a0D\u2217f(x)=limh\u21920\u2061f2(x+h)\u2212f2(x)h\u00a0where\u00a0f2(x)=(f(x))2\u00a0for example,\u00a0D\u2217f(x)=2x\u00a0if\u00a0f(x)=x,\u00a0D\u2217f(x)=2sin\u2061xcos\u2061x\u00a0if\u00a0f(x)=sin\u2061xD\u2217f(x)=2e2x\u00a0if\u00a0f(x)=ex"}]}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions\/539965"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=539965"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=539965"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}