solution_PM2_F10 - PROBLEM a F incl t he d erivative o f t...

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PROBLEM 2 a. Fincl the derivative of the function: f (:r) = r'sir]' 1 (c3") {'C^) = (. x r#* 3 l ' )'s,n'(€-l +xI*i s ,\i'[ et^ ) -r x ..{-.-{J = s,n-'(e,t*)+ x 3^ 3e (e=^)]' = .a- 'I Chcrtn nr \€- ,. 3'< \' teJ-- J r-#x b. Finrl thc derivative of the liruction: ,t(.t', - r,, (*lj t-). \ r/2't 2 / Hint: first u,se th,e pntpertit:s of the logarttlr.nr, to fin,d an easi,er e tpression for f . t,h,en, take th,e tk:riuati.ue. lf you" att,ernpt t,o tttAt: t.lt,e d,eri,uati,re tlit'ec.tl'y. tlt,r: proble.nr, wi.ll her:orn,e lortg uul rntn4tl'icatul. QCr\= s q c*t q 2 tx-t Ar . " 2 \ = l xl-\ I 0,x-z ln L*vr) - Qn JS. = O, (^+r) - ! Q" ('zx-2\ \ .<.- X'l-\
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D 4,* b/ - st\x Pfi -eB Ls14 , S,g .ftnn",f .;5'*i.> r'\'tt' E> fi.,rhdLj*€- l.,1ri u /u "g uu€ - Si\x '- e tec-X €'<.cXTA.n>( /\ ?- xeO igtpx ^+c) | .---- dr*1 rhtkF. L l' [+,'s,r,i-aL -[' : X _ToF, z 8n, l-- = lt* x-}C xs2'U -f ' d-rc ra -(,trn En c-e\X x-+., --zt€c.x ! n I \)( JLrcq A- Zx) x+o r r) {n ( \-ext =JUtrn g ' = -Alron x+o xio g = Atn e- \-ax = {t. x+() :) fruJ Lr*(+)) = -t - sif\ ( <.os-' (Tz\) + -tnr\-ax) /tw'tr&g--ea X e '= -2.* e'C X-)o 2- 9 I r' /'^ , \\ (t^ (3n/a )) lT'.-u dl,r1ry_is NoL + b< c,c$J\€ + '\ -Jl';t- ,nfr.r-q* ro-rqF" "t b*-'- ---\l Y t r 3f\ L - -.
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