{"id":1811,"date":"2024-05-29T09:49:26","date_gmt":"2024-05-29T00:49:26","guid":{"rendered":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/?p=1811"},"modified":"2024-06-17T12:52:40","modified_gmt":"2024-06-17T03:52:40","slug":"top-math2-2q4h-1","status":"publish","type":"post","link":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/?p=1811","title":{"rendered":"\u6570\u5b66II_2Q4H_1"},"content":{"rendered":"\n
\n
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 <\/span><\/td>\n <\/span><\/td>\n <\/span><\/td>\n <\/span><\/td>\nNext<\/span><\/a><\/td>\n<\/tr>\n
 <\/span><\/td>\n <\/span><\/td>\n <\/span><\/td>\n <\/span><\/td>\n\u518d\u751f\u30ea\u30b9\u30c8<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n\n\n\n\n\n\n\n
\u30c6\u30ad\u30b9\u30c8<\/span><\/td>\n\u6f14\u7fd2<\/span><\/td>\n\u6f14\u7fd2\u89e3\u7b54<\/span><\/td>\n\u8ab2\u984c<\/span><\/td>\n\u89e3\u8aac<\/span><\/td>\n<\/tr>\n
2Q4H_1<\/a><\/td>\n2Q4H_E1<\/a><\/td>\n2Q4H_ES1<\/a><\/td>\n2Q4H_K1<\/a><\/td>\n2Q4H_V1<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
<\/span> $y=|f(x)|$\u3000\u306e\u30b0\u30e9\u30d5\u3068\u5fae\u5206\u4e0d\u53ef\u80fd\u306a\u70b9\uff1d\uff1f <\/div>
\u65b9\u7a0b\u5f0f$y=f(x)=0$ \u3092\u89e3\u304d\u3001$x$\u8ef8\u3088\u308a\u4e0b\u5074\u306e\u90e8\u5206\u3092\u6298\u308a\u8fd4\u3059
\u5fae\u5206\u4e0d\u53ef\u80fd\u306a\u70b9\uff1d\u5c16\u3063\u305f\u70b9<\/span><\/div><\/div>
<\/span>Targets<\/div>
1. $y=|f(x)|$<\/span>\u306e\u30b0\u30e9\u30d5\u3092\u304b\u304d\u3001\u5fae\u5206\u4e0d\u53ef\u80fd\u306a\u70b9<\/span>\u3092\u6307\u6458\u3067\u304d\u308b <\/div><\/div> <\/div>\n
\n\n\n\n\n\n
2Q4H_2<\/a><\/td>\n2Q4H_E2<\/a><\/td>\n2Q4H_ES2<\/a><\/td>\n2Q4H_K2<\/a><\/td>\n2Q4H_V2<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n
<\/span> \u591a\u9805\u5f0f\u306e\u7a4d\u30fb\u5546\u30fb\u5408\u6210\u95a2\u6570\u306e\u5fae\u5206\uff1d\uff1f <\/div>
$(c)’=0$\u3001$(x)’=1$\u3001$(x^n)’=nx^{n-1}$\u3001$(f^n)’=nf’f^{n-1}$
$\\left(\\dfrac{1}{x^n}\\right)^{\\prime}=\\dfrac{-n}{x^{n+1}}$\u3001$\\left(\\dfrac{1}{g^n}\\right)^{\\prime}=\\dfrac{-ng’}{g^{n+1}}$
$(f\\cdot g)’=f’\\cdot g+f\\cdot g’$\u3001$\\left(\\dfrac{f}{g}\\right)^{\\prime}=\\dfrac{f’\\cdot g- f\\cdot g’}{g^2}$<\/span><\/div><\/div>
<\/span>Targets<\/div>
1. $y=f\\cdot g$<\/span>$\\quad$ 2. $y=\\dfrac{f}{g}$<\/span>$\\quad$3. $y=f^n$<\/span>$\\quad$4. $y=\\dfrac{1}{f^n}$<\/span>$\\quad$5. $y=\\sqrt[n]{f^m}$<\/span>
\u4ee5\u4e0a\u306e\u5fae\u5206\u304c\u3067\u304d\u308b<\/div><\/div> <\/div>\n
\n\n\n\n\n\n\n\n
2Q4H_3<\/a><\/td>\n2Q4H_E3<\/a><\/td>\n2Q4H_ES3<\/a><\/td>\n2Q4H_K3<\/a><\/td>\n2Q4H_V3<\/a><\/td>\n<\/tr>\n
 <\/td>\n <\/td>\n <\/td>\n <\/td>\n2Q4H_pf3<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n
<\/span> \u5bfe\u6570\u95a2\u6570(log) \u306e\u5fae\u5206\uff1d\uff1f <\/div>
$({\\mathrm{log}}x)’=({\\mathrm{log}}|x|)’=\\dfrac{1}{x}$<\/span>\u3001$({\\mathrm{log}}f)’=\\dfrac{f’}{f}$<\/span><\/div><\/div>
<\/span>Targets<\/div>
1. $y={\\mathrm{log}}f, {\\mathrm{log}}|f|$<\/span>$\\quad$2. $y=g\\cdot {\\mathrm{log}}f, \\dfrac{{\\mathrm{log}}f}{g}$<\/span>$\\quad$3. $y=({\\mathrm{log}}\u3092\u542b\u3093\u3060\u5f0f)^n$<\/span>
\u4ee5\u4e0a\u306e\u5fae\u5206\u304c\u3067\u304d\u308b<\/div><\/div> <\/div>\n
\n\n\n\n\n\n
2Q4H_4<\/a><\/td>\n2Q4H_E4<\/a><\/td>\n2Q4H_ES4<\/a><\/td>\n2Q4H_K4<\/a><\/td>\n2Q4H_V4<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n
<\/span>\u5bfe\u6570\u5fae\u5206\u306e\u5fdc\u7528 $(f^ng^m)'=?$ \u3001$(f^n\/g^m)'=?$ \u3001 $(e^x\u3001a^x \u3092\u542b\u3093\u3060\u5f0f)'=?$<\/div>
\u5bfe\u6570\u5fae\u5206\uff1a $y’=y({\\mathrm{log}}y)’$<\/span>\u3001\u6307\u6570\u95a2\u6570\u306e\u5fae\u5206\uff1a$e^f=f’e^f$<\/span>\u3001$a^f=f’a^f{\\mathrm{log}}a$<\/span>
$\uff08f^ng^m)’=f^{n-1}g^{m-1}(nf’g+mfg’)$<\/span>
$\\left( \\dfrac{f^n}{g^m} \\right)^{\\prime}=\\dfrac{f^{n-1}(nf’g-mfg’)}{g^{m+1}} $<\/span><\/div><\/div>
<\/span>Targets<\/div>
1. $f^ng^m$<\/span>\u30012. $\\dfrac{f^n}{g^m}$<\/span>\u30013. ($e^x$\u3001$a^x$\u3092\u542b\u3093\u3060\u5f0f)<\/span>\u306e\u5fae\u5206\u304c\u3067\u304d\u308b<\/div><\/div> <\/div>\n\n\n\n\n\n\n
2Q4H_5<\/a><\/td>\n2Q4H_E5<\/a><\/td>\n2Q4H_ES5<\/a><\/td>\n2Q4H_K5<\/a><\/td>\n2Q4H_V5<\/a><\/td>\n<\/tr>\n
 <\/td>\n <\/td>\n <\/td>\n <\/td>\n2Q4H_pf5<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
<\/span> $sin\u03b8\/\u03b8 \u2192? (\u03b8 \u2192 0)$ \u3001\u4e09\u89d2\u95a2\u6570\u306e\u5fae\u5206 $(sinx)'=?$\u3001$(cosx)'=?$\u3001$(tanx)'=?$<\/div>
${\\displaystyle{\\lim_{\\theta\\to 0}}}\\dfrac{{\\mathrm{sin}}\\theta}{\\theta}={\\displaystyle{\\lim_{\\theta\\to 0}}}\\dfrac{\\theta}{{\\mathrm{sin}}\\theta}=1$<\/span>\u3001${\\displaystyle{\\lim_{\\theta\\to 0}}}\\dfrac{{\\mathrm{tan}}\\theta}{\\theta}={\\displaystyle{\\lim_{\\theta\\to 0}}}\\dfrac{\\theta}{{\\mathrm{tan}}\\theta}=1$<\/span>
$({\\mathrm{sin}}x)’={\\mathrm{cos}}x$<\/span>\u3001$({\\mathrm{sin}}f)’=f'{\\mathrm{cos}}f$<\/span>
$({\\mathrm{cos}}x)’=-{\\mathrm{sin}}x$<\/span>\u3001$({\\mathrm{cos}}f)’=-f'{\\mathrm{sin}}x$<\/span>
$({\\mathrm{tan}}x)’=\\dfrac{1}{{\\mathrm{cos}}^2x}$<\/span>\u3001$({\\mathrm{tan}}f)’=\\dfrac{f’}{{\\mathrm{cos}}^2f}$<\/span><\/div><\/div>
<\/span>Targets<\/div>
1. ${\\displaystyle{\\lim_{\\theta\\to 0}}}\\dfrac{{\\mathrm{sin}}\\theta}{\\theta}={\\displaystyle{\\lim_{\\theta\\to 0}}}\\dfrac{\\theta}{{\\mathrm{sin}}\\theta}=1$<\/span>\u3001${\\displaystyle{\\lim_{\\theta\\to 0}}}\\dfrac{{\\mathrm{tan}}\\theta}{\\theta}={\\displaystyle{\\lim_{\\theta\\to 0}}}\\dfrac{\\theta}{{\\mathrm{tan}}\\theta}=1$<\/span>\u3092\u7528\u3044\u3066\u6975\u9650\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
2. ${\\mathrm{sin}}x$<\/span>\u3001 ${\\mathrm{cos}}x$<\/span>\u3001${\\mathrm{tan}}x$<\/span>\u3092\u542b\u3093\u3060\u5f0f\u306e\u5fae\u5206\u304c\u3067\u304d\u308b <\/div><\/div> <\/div>\n
\n\n\n\n\n\n\n\n
2Q4H_6<\/a><\/td>\n2Q4H_E6<\/a><\/td>\n2Q4H_ES6<\/a><\/td>\n2Q4H_K6<\/a><\/td>\n2Q4H_V6<\/a><\/td>\n<\/tr>\n
 <\/td>\n <\/td>\n <\/td>\n <\/td>\n2Q4H_pf6<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n
<\/span> \u9006\u4e09\u89d2\u95a2\u6570\u306e\u5fae\u5206 $($Sin^[-1] $x)'=?$\u3001$($Cos^[-1] $x)'=?$\u3001$($Tan^[-1] $x)'=?$<\/div>
$({\\mathrm{Sin}}^{-1}x)’=\\dfrac{1}{\\sqrt{1-x^2}}$\u3001$({\\mathrm{Cin}}^{-1}x)’=\\dfrac{-1}{\\sqrt{1-x^2}}$\u3001$({\\mathrm{Tan}}^{-1}x)’=\\dfrac{1}{x^2+1}$
$\\left({\\mathrm{Sin}}^{-1}\\dfrac{x}{a}\\right)^{\\prime}=\\dfrac{1}{\\sqrt{a^2-x^2}}$\u3001$\\left({\\mathrm{Cin}}^{-1}\\dfrac{x}{a}\\right)^{\\prime}=\\dfrac{-1}{\\sqrt{a^2-x^2}}$\u3001$\\left({\\mathrm{Tan}}^{-1}\\dfrac{x}{a}\\right)^{\\prime}=\\dfrac{a}{x^2+a^2}$<\/span><\/div><\/div>
<\/span>Targets<\/div>
1. ${\\mathrm{Sin}}^{-1}x$<\/span>\u3001${\\mathrm{Cos}}^{-1}x$<\/span>\u3001${\\mathrm{Tan}}^{-1}x$<\/span>\u3092\u542b\u3093\u3060\u5f0f\u306e\u5fae\u5206\u304c\u3067\u304d\u308b
2.\u4eca\u307e\u3067\u5b66\u3093\u3060\u5fae\u5206\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u5fae\u5206\u8a08\u7b97\u306e\u7dcf\u5408\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b<\/div><\/div> <\/div>\n
\n\n\n\n\n\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\nNext<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

        Next         \u518d\u751f\u30ea\u30b9\u30c8 \u30c6\u30ad\u30b9\u30c8 \u6f14\u7fd2 \u6f14\u7fd2\u89e3\u7b54 \u8ab2\u984c \u89e3\u8aac 2Q4H_1 2Q4H_E1 2Q4H_ES1 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[42,14,4,8,34],"tags":[],"class_list":["post-1811","post","type-post","status-publish","format-standard","hentry","category-si","category-top","category-math2","category-math2-2q","category-math2-2q4h-1"],"_links":{"self":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/1811","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1811"}],"version-history":[{"count":114,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/1811\/revisions"}],"predecessor-version":[{"id":2221,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/1811\/revisions\/2221"}],"wp:attachment":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1811"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1811"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1811"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}