{"id":939,"date":"2025-11-21T16:18:22","date_gmt":"2025-11-21T07:18:22","guid":{"rendered":"http:\/\/saegil-lab.kr\/?p=939"},"modified":"2026-03-11T19:33:58","modified_gmt":"2026-03-11T10:33:58","slug":"%ec%a7%80%ec%88%98%ed%95%a8%ec%88%98-latexpage-fxax%ec%9d%98-%eb%af%b8%eb%b6%84","status":"publish","type":"post","link":"https:\/\/saegil-lab.kr\/?p=939","title":{"rendered":"\uc9c0\uc218\ud568\uc218 \"f(x)=a^x\"\uc758 \ubbf8\ubd84"},"content":{"rendered":"\n

  <\/span>   <\/span>\"\[ f(x) = a^x \]\"<\/p><\/p>\n\n\n\n

  <\/span>   <\/span>\"\begin{align*}f'(x) &= \lim_{h \rightarrow 0} \frac{a^{x+h} - a^x}{h} \\&= \lim_{h \rightarrow 0}\frac{a^x(a^h - 1)}{h}\\&= a^x \times \lim_{h \rightarrow 0}\frac{a^h - 1}{ h}\end{align*}\"<\/p><\/p>\n\n\n\n

\"a^h - 1 =t\"\ub77c\uace0 \ud558\uba74 \"a^h = 1 + t\"\uac00 \ub418\uba70 \uc774 \uc2dd\uc758 \uc591\ubcc0\uc5d0 \uc790\uc5f0\ub85c\uadf8\ub97c \ucde8\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ \ln a^h = h \ln a = \ln (1+t) \]\"<\/p><\/p>\n\n\n\n

  <\/span>   <\/span>\"\[h = \frac{\ln (1+t)}{\ln a} \]\"<\/p><\/p>\n\n\n\n

\"h \rightarrow 0\"\uc77c \ub54c \"t \rightarrow 0\"\uc774 \ub418\ubbc0\ub85c \"f'(x)\"\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \ud45c\uc2dc\ud560 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n

  <\/span>   <\/span>\"\begin{align*}f'(x) &= a^x \times \lim_{t \rightarrow 0} \frac{t}{\frac{\ln (1+t)}{\ln a}} \\&= a^x \ln a \times \lim_{t \rightarrow 0} \frac{1}{\frac{1}{t} \ln(1+t)} \\&= a^x \ln a \times \lim_{t \rightarrow 0} \frac{1}{\ln(1+t)^\frac{1}{t}} \\&= a^x \ln a \times \frac{1}{\ln e} \\&= a^x \ln a\end{align*}\"<\/p><\/p>\n","protected":false},"excerpt":{"rendered":"

        \ub77c\uace0 \ud558\uba74 \uac00 \ub418\uba70 \uc774 \uc2dd\uc758 \uc591\ubcc0\uc5d0 \uc790\uc5f0\ub85c\uadf8\ub97c \ucde8\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.         \uc77c \ub54c \uc774 \ub418\ubbc0\ub85c \ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \ud45c\uc2dc\ud560 \uc218 \uc788\ub2e4.    <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[70,71],"class_list":["post-939","post","type-post","status-publish","format-standard","hentry","category-13","tag-70","tag-71"],"_links":{"self":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/939","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=939"}],"version-history":[{"count":14,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/939\/revisions"}],"predecessor-version":[{"id":1006,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/939\/revisions\/1006"}],"wp:attachment":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=939"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=939"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=939"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}