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U y v( o t) A y R T g Ēv ܂ B A c A q 炲 ҂܂Ŋy ߂ B c t E ۈ牀 v O 1 E w Z Z u ӏ܉ ͍ N ł ߂悤 Ǝv Ă ̂ v. Proof lnexy = xy = lnex lney = ln(ex ·ey) Since lnx is onetoone, then exy = ex ·ey 1 = e0 = ex(−x) = ex ·e−x ⇒ e−x = 1 ex ex−y = ex(−y) = ex ·e−y = ex · 1 ey ex ey • For r = m ∈ N, emx = e z }m { x···x = z }m { ex ···ex = (ex)m • For r = 1 n, n ∈ N and n 6= 0, ex = e n n x = e 1 nx n ⇒ e n x = (ex) 1 • For r rational, let r = m n, m, n ∈ N. Ȃ݂ɁA13 ł̋~ o C x g i ŕ m } E H C x g ̉ӏ j ŁA ǂ Ă E Ă ܂ ́A11 ŃI X g @ ~ o O ɁA ̖ J Ă Ƃ E ߂܂ B 邱 Ƃŏ 13 ̋~ o C x g ܂ B ̕t ߂ɃI X g @ ̎p ͂ ܂ i E Ă 킯 ł͂ ܂ j A14 ̊K i ɍ Ă ̂ŁA A13 ł ~ o Ă 邱 ƂɂȂ ܂ B.

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Smith, R Snodgrass, S F Terrell, D L Thmnas, B J Clit' kiflc cam x if' RIFLE TEAM LETTERMEN Back row to nght Col Raymond Orr George T Baker Kenneth L Flelder C W Levmgston V K Cameron Thomas E Werlm Bemgno Leal Col Stanley Y Kennedy Marcel Kenty Vlctor D Everett Not pictured Mrlton L Bell Walks H Eckhoff john T Hom HEARST TROPHY MATCH. TPromotion e B v V ̓C x g A C x g c i o V ӂ ӂ E ݁E L N ^ V E p t H } X j ̊ E E ̔ E ^ ̉ Ђł B. Find dy/dx e^(x/y)=xy Differentiate both sides of the equation Differentiate the left side of the equation Tap for more steps Differentiate using the chain rule, which states that is where and Tap for more steps To apply the Chain Rule, set as.

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HDC R t H g n E X v U X v O J j o ɏo W ܂ I ̃y W B F 09 N3 i j10 `18 ^09 N3 21 i y j10 `18 ꏊ F JP _ ˉw o o Ă C x g ̂P F d X g u ŏĂ s U I H i3 1 j. ̔ e J s A E g l y e l EJr X ^ C X g l E X ^ C X g l E e t l z 哇 A T ˁA 搼 哇 B ׋ R N Q w ЊO ̔ e B ꏏ ɐ グ Ă X ^ b t W Ă ܂. May 16, 11 254 CHAPTER 13 CALCULUS OF VECTORVALUED FUNCTIONS (LT CHAPTER 14) Use a computer algebra system to plot the projections onto the xy and xzplanes of the curve r(t) = t cost,tsin t,t in Exercise 17 In Exercises 19 and , let r(t) = sin t,cost,sin t cos2t as shown in Figure 12 y x z FIGURE 12 19.

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