Exercise:
multicols enumerate item %% ds fx eul^sin x item %% ds px lnbigsin x^big item %% ds at ln fract item %% ds gx fracarcsin x item %% ds Et eul^eul^t item %% ds Fvarphi rvarphi sin varphi cos varphi item %% ds gy log_ tan y item %% ds fx log_pi a-x^ item %% ds gz z^ tanz+ item %% ds fz eul^. item %% ds fz z^. item %% ds fx .^x item %% ds hu x^u-x item %% ds hs s sqrtss item %% ds Ia fraca ln left| fraclambda - alambda + aright| item %% ds kr fracln sqrt+r^sqrt+r^ item %% ds Hs arctan^- s^ item %% ds Phia fraca ln x^a item %% ds Cb ln left|tan leftfracb + fracpirightright| item %% ds Kx fracx sqrta^ - x^ + fraca^ arcsin fracx|a| item %% ds fx fracsqrtxx^ sqrtx item %% ds gx sqrtxsqrtxsqrtxsqrtx item %% ds Flambda ln fracsin lambdaeul^lambda item %% ds Fx _k^n c_k x^k item %% ds Hlambda fracsinlambdaln lambda sqrt+eul^lambda item %% ds dalpha fracln cos alphapi-alpha^n item %% ds Rv sin v^arctan sqrtxv item %% ds alpha s ln biglnsin sbig item %% ds fx cot x^cos x item %% ds Phit sqrtsinbigvarphitbig item %% ds zetaa frac-b + sqrtb^-aca item %% ds gammav fracsqrt-leftfracvcright^ item %% ds Ii i^i^i item %% ds Glambda sqrtlog_tan lambda enumerate multicols bigskip Leite die folgen Funktionen n mal ab n gerade: medskip multicols enumerate setcounterenumi item %% ds sinhz fraceul^z - eul^-z item %% ds fx eul^varepsilon x + eul^x item %% ds gxi ln xi item %% ds omegat sin pi t enumerate multicols

Solution:
enumerate itemtextbf fxeul^sin x f'x frameboxcos x eul^sin x rulelinewidth.pt itemtextbf pxlnsin x^ p'x dfracsin x^ cos x^ xxdfraccos x^sin x^ frameboxdfracxtan x^ xcot x^ rulelinewidth.pt itemtextbf atln!leftdfractrightoverset*-ln t a'tdfracfract dfrac-t^dfrac-tt^ framebox-dfract quad einfacher: zuerst Umformung * rulelinewidth.pt itemtextbf gxdfracarcsin xarcsin^- g'x-arcsin x^- dfracsqrt-x^ framebox-dfracsqrt-x^arcsin ^ x rulelinewidth.pt itemtextbf Eteul^eul^t E't frameboxeul^eul^teul^t frameboxeul^e^t+t rulelinewidth.pt itemtextbf Fphirphisinphicosphihfill* sinphicosphisin phi ed F'phir'phisinphicosphi+rphicosphicosphi+rphisinphi-sinphi textframeboxr'phisinphicosphi+rphicos^phi-sin^phi overset*r'phidfracsinphi+rphicosphi ed rulelinewidth.pt itemtextbf gylog_ tan y dfracln lntan y g'ydfracln dfractan ydfraccos^ y dfracln dfraccos ysin ydfraccos^ y frameboxdfracln sin y cos y dfracln sin y rulelinewidth.pt itemtextbf fx log_pi a-x^dfraclnbiga-x^biglnpidfraclnpi lna-x f'x dfraclnpidfraca-x - framebox dfracx-alnpi rulelinewidth.pt itemtextbf gzz^tanz!+! ed g'zztanz!+!+z^+tan^z!+! textframeboxz^+ztanz!+!+z^tan^z!+! ed rulelinewidth.pt itemtextbf fze^. ed f'ztextframebox ed rulelinewidth.pt itemtextbf fzz^. ed f'ztextframebox.z^. ed rulelinewidth.pt itemtextbf fx.^xbigeul ^ln .big^xeul^xln . f'xeul^xln . ln . frameboxln . .^x rulelinewidth.pt itemtextbf hux^u-xeul^ln xu-x h'ueul^ln xu-xln x frameboxln x x^u-x rulelinewidth.pt itemtextbf hsssqrtsss^+fracss^fracs+se^ln s fracs+s ed h'se^ln s fracs+s leftdfracs dfracs+s - dfracs^ ln s right s^fracs+s leftdfracs+s^-dfracln ss^right ssqrtss dfracs+-ln ss^textframebox sqrtss left+dfrac-ln ssright ed rulelinewidth.pt itemtextbf ds Ia fraca ln left| fraclambda - alambda + aright| I'a-dfraca^ln left| dfraclambda!-!alambda!+!aright|+ dfracadfraclambda!+!alambda!-!a dfrac-lambda!+!a-lambda!-!alambda!+!a^ framebox-dfracaleftdfracaln left|dfraclambda!-!a lambda!+!aright| + dfraclambdalambda!+!a^right rulelinewidth.pt itemtextbf krdfracln sqrt+r^sqrt+r^ ed k'rdfraccfracsqrt+r^ cfracsqrt+r^ rsqrt+r^-ln sqrt+r^ cfracsqrt+r^ r+r^ dfraccfracrsqrt+r^-dfraclnsqrt+r^sqrt+r^r+r^ textframeboxr dfrac-lnsqrt+r^+r^^frac ed rulelinewidth.pt itemtextbf Hsarctan^- s^ H's-arctan^-s^dfrac+s^^ s framebox-dfracs+s^bigarctan^s^big rulelinewidth.pt itemtextbf Phiadfracaln x^adfraca aln xln x Phi'a framebox rulelinewidth.pt itemtextbf Cbln left|tan leftdfracb+dfracpirightright| hfill * wegen sin phisinphicosphi ed C'bdfractan leftdfracb+dfracpiright cfraccos^leftdfracb+dfracpirightdfrac dfracdfraccos leftdfracb+dfracpirightsin leftdfracb+dfracpiright cfraccos^leftdfracb+dfracpiright dfracsinleftdfracb+dfracpirightcosleftdfracb+dfracpirightoverset* dfracsinbigb+dfracpibigtextframeboxdfraccos b ed rulelinewidth.pt itemtextbf Kxdfracxsqrta^-x^+dfraca^arcsindfracx|a| ed K'xdfracsqrta^-x^+dfracxdfrac-xsqrta^-x^+ dfraca^dfracsqrt-leftdfracx|a|right^dfraca dfracsqrta^-x^-dfracx^sqrta^-x^+dfracasqrtdfraca^-x^a^ dfracsqrta^-x^-dfracx^sqrta^-x^+dfraca^sqrta^-x^ dfracsqrta^-x^+dfraca^-x^sqrta^-x^dfracsqrta^-x^+dfracsqrta^-x^ textframeboxsqrta^-x^ ed rulelinewidth.pt itemtextbf fxdfracsqrtxx^sqrtxx^frac x^- x^-frac x^frac--x^-frac f'xtextframebox-dfrac x^ -frac-dfracsqrtx^ rulelinewidth.pt itemtextbf gxsqrtxsqrtxsqrtxsqrtx x^left frac+frac+frac+frac rightx^frac g'xdfrac x^frac- text frameboxdfrac x^-fracdfracsqrtx dfracsqrtsqrtsqrtsqrtx rulelinewidth.pt itemtextbf Flambda ln dfracsin lambdaeul^lambdalnsinlambda-lneul^lambdalnsinlambda-lambda F'lambdadfraccoslambdasinlambda- frameboxcotlambda- rulelinewidth.pt itemtextbf ds Fx _k^n c_k x^kc_+c_x+c_x^+c_x^+dots+c_nx^n ds F'x c_+c_x+c_x^+dots+nc_nx^n- frameboxds_k^n k c_k x^k- rulelinewidth.pt itemtextbf ds Hlambda fracsinlambdaln lambda sqrt+eul^lambda ds H'lambdadots frameboxdsfraccoslambdalnlambdasqrt+eul^lambda- sinlambdaleftdfraclambdasqrt+eul^lambda+lnlambdadfraceul^lambdasqrt+eul^lambdaright ln^ lambda+eul^lambda rulelinewidth.pt itemtextbf ds dalpha fracln cos alphapi-alpha^n ds d'alpha dots frameboxdsfracnln cos alpha-pi-alphatanalphapi-alpha^n+ rulelinewidth.pt itemtextbf ds Rv sin v^arctan sqrtxv ds R'v dots frameboxsin v^arctansqrtxvleftcot varctansqrtxv+dfracxlnsin vsqrtxv+xvright rulelinewidth.pt itemtextbf ds alpha s ln biglnsin sbig ds alpha's dots frameboxdfraccot xlnsin s rulelinewidth.pt itemtextbf ds fx cot x^cos xfractan x^cos xfraccos x^cos xsin x^cos x ed ds f'x frac-sin^ x^cos x-cos^ x^cos xsin^ x^cos xleftx^cos xright' -fracsin^ x^cos x big eul^ln xcos x big' -fracx^cos xsin^ x^cos x leftfraccos xx-ln x sin xright textframeboxfracx^cos xsin^ x^cos x leftln x sin x-fraccos xxright ed rulelinewidth.pt itemtextbf Phitsqrtsinphit Phi'tdfracsqrtsinphit cosphit dotphit dfracsqrtsinphitcosphit dotphit sinphit frameboxdfracsqrtsinphittanphit dotphit rulelinewidth.pt itemtextbf zetaadfrac-b+sqrtb^-aca zeta'a text framebox dfracdfrac-acsqrtb^-ac+b-sqrtb^-aca^ rulelinewidth.pt itemtextbf gammavdfracsqrt-leftdfracvcright^left-leftdfracvcright^right^-frac gamma'v-dfrac left-leftdfracvcright^right^-frac dfrac-vc^ frameboxdfracvc^ left-leftdfracvcright^right^frac dfracvc^sqrt-leftdfracvcright^ rulelinewidth.pt item textbf ds Ii i^i^ii^i^ieul^i^iln ieul^eul^iln iln i ds Ii eul^eul^iln iln i left fraci eul^iln i + ln i leftln i+ i fracirightright frameboxi^i^i i^i left dfraci+ln iln i+ right rulelinewidth.pt itemtextbf ds Glambda sqrtlog_tan lambdaleftfracln lntanlambdaright^frac ed ds G'lambda fracleftfracln lntanlambdaright^ -frac fracln fractan lambda fraccos^ lambda fracbiglog_tanlambdabig^ -frac fracln fracsin lambda cos lambda textframeboxdfracrulemm.mmdfracln sin lambdacos lambdasqrtlog_^tanlambda ed rulelinewidth.pt itemtextbf ds sinhz fraceul^z - eul^-z ds sinh^nz framebox dfraceul^z - eul^-zqquad f"ur gerade n rulelinewidth.pt itemtextbf ds fx eul^varepsilon x + eul^x ds f^nx framebox varepsilon^neul^varepsilon x + eul^xqquad gilt auch f"ur ungerade n rulelinewidth.pt itemtextbf ds gxi ln xi ds g^nxi framebox -n!-!! xi^-nqquad gilt auch f"ur ungerade n rulelinewidth.pt itemtextbf ds omegat sin pi t ds omega^nt framebox -^fracn pi^nsin pi tqquad f"ur gerade n enumerate