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数学 高校生

赤丸で印をつけた(3)について… 微分したこたえを4でくくっても○ですか⁇

320 基本 例題 199 導関数の計算 (2) 展開してから微分 次の関数を微分せよ。宅 (1) y=(x+1)(x-3) (2)y=(2x+1)3 (3) y=(x²-2x+3) (4) y= (4x-3) (2x+3) (k, 指針 積や累乗の形のものは、 展開してから,公式を使って微分すればよい。 (x)=xn は正の整数), {kf(x)+1g(x)}'=kf'(x)+1g'(x) 別解のように, 次ページで紹介する, 次の公式①、②を利用してもよい。 ① {f(x)g(x)}=f(x)g(x)+f(x)g' (x) (積の導関数の公式) ② {(ax+b)"}'=n(ax+b)"' (ax+b)' 一般に ({f(x)}")'=n{f(x)}"'f'(x) (1) y=x'+x2-3x-3 nは自然数 は定数 解答 よって y'=3x2+2x-3・1=3x2+2x-3 (2) y=(2x)+3(2x)・1+3・2x・12+1=8x3+12x2+6x+1 よって y'=8・3x2+12・2x+6・1=24x2+24x+6 (+) (3) y=(x2)2+(-2x)+32+2・x2・(-2x)+2・(-2x)・3+2・3・x2 =x4-4x3+10x²-12x+9 よって よって y′=4x3-4・3x2+10・2x-12・1=4x-12x2+20x-12_ (4) y=(16x²-24x+9)(2x+3)=32x³-54x+274(x²-22+20) y'=32・3x2-54・1=96x2-54 別解 (1) y'=(x+1)(x-3)+(x+1)(x-3)=1(x2-3)+(x+1) ・2x =3x²+2x-3= mil (2) y'=3(2x+1)3-1(2x+1)=3(2x+1)^2=6(2x+1) (3)y'=2(x²-2x+3)2-1(x²-2x+3)=2(x²-2x+3) ・(2x-2) =4(x-1)(x²-2x+3) (4) y'={(4x-3)^^(2x+3)+(4x-3)^(2x+3)、 ={2(4x-3)^(4x-3)^}(2x+3)+(4x-3)^ ・2 まず、積の導関数。 ={2(4x-3)・4}(2x+3)+2(4x-3)²=2(4x-3){4(2x+3)+(4x-3)} =2(4x-3)(12x+9)=6(4x-3)(4x+3) 参考 別解の(2)~(4)の結果は,展開すると上の解答と同じになる。 ■ 公式 ① {f(x)g(x)}'=f'(x)g(x)+f(x)g'(x), ②{(ax+b)"}'=n(ax+b)"-1 (2x+ 式を展開せずに計算でき

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英語 高校生

やじるし部分のこたえを教えてほしいです

New Words ☐ canned [kænd] ☐ feed [fi:d] newsletter [n(jú:zlètǝr] specially [spéfǝli] emergency [imardzǝnsi] freshly [fréfli] ☐ originate [aridzanéit] baker [beikar ☐ victim [viktim] Odistribute [distribju:t] depressing [diprésiŋ] You are reading a newsletter article about canned bread. Canned Bread to Feed the rid Have you ever heard of canned bread? This specially pa bread is designed as emergency food. When you open the can tastes as delicious as freshly baked bread. The idea of canned bread originated in the Great Hans Awaji Earthquake of 1995. Immediately after the earthqua a baker named Akimoto Yoshihiko baked 2,000 rolls and s them to the victims. A few days later, he got bad news. Half the rolls went bad before they could be distributed to people need. Therefore, they were thrown away. Akimoto G1 disappointed to hear that. G1 G1 A little while later, one of the earthquake victims said to hi "It was so depressing to have only hard biscuits to eat. I'd like to create bread that keeps for a long time but stays saf G1 Akimoto decided to rise to the challenge. 72 1. What did Mr. Akimoto do immediately after the earthquake? 2. What happened to the rolls that Mr. Akimoto sent? 3. What did Mr. Akimoto decide to create? Opinion 1. Have you ever eaten canned bread? If you have, how did it taste? If you haven't, what do you think it tastes like? go bad ex. The milk will go bad if you don't put it in the fridge. rise to the challenge ex. Our team rose to the challenge and won the tournament.

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