![]() ![]() *** 科目 *** 数Ⅰ・A数Ⅱ・B数Ⅲ高卒・大学初年度 *** 単元 *** 複素数平面二次曲線媒介変数表示と極座標 数列の極限関数導関数不定積分定積分 行列1次変換 ※高校数学Ⅲの「微分・導関数」について,このサイトには次の教材があります.
この頁へGoogleやYAHOO ! などの検索から直接来てしまったので「前提となっている内容が分からない」という場合や「この頁は分かったがもっと応用問題を見たい」という場合は,他の頁を見てください. が現在地です. ↓微分係数,連続,微分可能 ↓積の微分 ↓商,分数関数の微分 ↓合成関数の微分 ↓無理関数の微分 ↓媒介変数表示のときの微分法 ↓同(2) ↓陰関数の微分法 ↓重要な極限値(1)_三角関数 ↓三角関数の微分 ↓三角関数の微分(2)-現在地 ↓指数関数,対数関数の微分 ↓対数微分法 ↓微分(総合演習) ↓漸近線の方程式 ↓同(2) ↓凹凸と変曲点 ↓総合--増減.極値.凹凸.変曲点.漸近線(1) ↓分数関数の増減.極値.漸近線 グラフの概形と漸近線(一覧) |
【三角関数の微分公式】
(*4)は教科書には出ていない
習う生徒と習わない生徒がいて,よく質問がある記号
【微分法で使う公式】
(補足)積の微分法 商の微分法 合成関数の微分法 逆関数の微分法 (5)~(7)については,3文字目の逆数と覚えるとよい
(セカントx) sec x=1/cos x
(コタンジェントx) cot x=1/tan x (コセカントx) cosec x=1/sin x
アメリカでは,小文字3字で,csc x=1/sin x
の記号が使われる.⇒ Excel,TEXなどでは |
【例題1】 次の関数を微分してください.
1.1)
(解答)により |
1.2)
(解答)により ※(6)を用いて |
【問題1】 次の関数を微分してください.(選択肢の中から正しいものを1つクリック)
(1)
|
(2)
|
(3)
|
(4)
|
【問題2】 次の関数について
(1)
|
(2)
|
(3)
|
(4)
逆関数の微分法(11)を使う
公式(*4)によりだから 問題によっては,このまま答にしてよいこともある.この問題では,一致する選択肢がないから,変形する. 数学Ⅰ,Ⅱの三角関数の相互関係から の両辺を したがって |
大学入試問題(やさしい方)
【問題3】 次の関数を微分せよ.
(3.1)
解説を読む
(2014年宮崎大)
|
(3.2)
解説を読む
(2011年茨城大)
|
(3.3)
解説を読む
(2005年佐賀大)
|
※次の問題は対数微分法を学んでから行うとよい
(3.4)
解説を読む
(2016年岡山県立大)
|
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