Exercise:
nprvmulticols abclist %a abc displaystyle _^ x^ cosx^ ddx %b abc displaystyle _^ x texte^x^ ddx %c abc displaystyle _^ fracx + ddx %d abc displaystyle _^ fracxx^ + ddx %e abc displaystyle sinx + ddx %f abc displaystyle _^ fracxx^ + ^ ddx %g abc displaystyle fracx^x^ + ddx %h abc displaystyle fracsqrt - x ddx %i abc displaystyle x lnx^ + ddx abc displaystyle fracxsqrtx^ + ddx %k abc displaystyle _texte^texte^ fracx lnx ddx %l abc displaystyle _^fracpi fraccos^x ddx abc displaystyle x^ sqrtx^ + ddx abc displaystyle fracxx^ - ddx %o abc displaystyle _^ fracx + ^ ddx %p abc displaystyle _^fracln fractexte^x + texte^x ddx abc displaystyle tanx sec^x ddx abc displaystyle fracsqrtx - ddx %s abc displaystyle _^ x sqrt + x^ ddx %t abc displaystyle fracx^x^ + ^ ddx %u abc displaystyle fracsqrt - x ddx %v abc displaystyle _^ fracxsqrtx^ + ddx %w abc displaystyle frac + x + ^ ddx %x abc displaystyle _^frac ln fractexte^xtexte^x + ddx abclist nprvmulticols

Solution:
abclist %a abc Fx tcbhighmathaufgabe_^ x^cosx^ dd x substitutiony:x^quad dd yx^dd x _^ cosy dd y leftsinyright_^ sin-sin tcbhighmathloesungsin %b abc Fx tcbhighmathaufgabe_^ x mathrm e^x^dd x substitutiony:x^quad dd yxdd x frac_^ mathrm e^ydd y frac lefttexte^yright_^ tcbhighmathloesungfraclefttextright %c abc Fx tcbhighmathaufgabe_^ fracx+dd x substitutiony:x+quad dd ydd x frac_^ fracydd y frac leftlnyright_^ fracleftln -ln right tcbhighmathloesungfracln %d abc Fx tcbhighmathaufgabe_^ fracxx^+dd x substitutiony:x^+quad dd yxdd x _^ fracydd y leftlnyright_^ leftln-ln right tcbhighmathloesungln %e abc Fx tcbhighmathaufgabe sinx+dd x substitutiony:x+quad dd ydd x frac sinydd y -frac cosy + C tcbhighmathloesung-tfraccosx++C %f abc Fx tcbhighmathaufgabe_^ fracxx^+^dd x substitutiony:x^+quad dd yxdd x frac_^ y^-dd y fracleft-y^-right_^ fracleft-frac+fracright frac-frac tcbhighmathloesungfrac %g abc Fx tcbhighmathaufgabe fracx^x^+dd x substitutiony:x^+quad dd yx^dd x frac fracydd y frac lny + C tcbhighmathloesungtfracln|x^+|+c %h abc Fx tcbhighmathaufgabe fracsqrt-xdd x substitutiony:-xquad dd y-dd x -frac y^-fracdd y tcbhighmathloesung-sqrt-x+c %i abc Fx tcbhighmathaufgabe xlnx^+dd x substitutiony:x^+quad dd yxdd x frac lnydd y fracbiglyln y-ybigr+c tcbhighmathloesungtfracbiglx^+lnx^+-x^+bigr+c %j abc Fx tcbhighmathaufgabe fracxsqrtx^+dd x substitutiony:x^+quad dd yxdd x frac y^-fracdd y tcbhighmathloesungsqrtx^++c %k abc Fx tcbhighmathaufgabe_texte^texte^ fracxln xdd xqquad x substitutiony:ln xquad dd yfracxdd x _^ fracydd y tcbhighmathloesungln|ln x|+c %l abc Für diese Aufgabe muss man die Ableitung des Tangens kennen tanrightarrowfraccos^. Fx tcbhighmathaufgabe_^fracpi fraccos^xdd x sec^xdd x substitutiony:xquad dd ydd x frac_^fracpi sec^ydd y tcbhighmathloesungtfractanx+c %m abc Fx tcbhighmathaufgabe x^sqrtx^+dd x substitutiony:x^+quad dd yx^dd x frac y^fracdd y tcbhighmathloesungtfracx^+^/+c %n abc Fx tcbhighmathaufgabe fracxx^-dd x substitutiony:x^-quad dd yxdd x frac fracydd y tcbhighmathloesungtfracln|x^-|+c %o abc Fx tcbhighmathaufgabe_^ fracx+^dd x substitutiony:x+quad dd ydd x frac_^ y^-dd y tcbhighmathloesung-fracx++c %p abc Fx tcbhighmathaufgabe_^frac ln fracmathrm e^x+mathrm e^xdd x substitutiony:+mathrm e^xquad dd ymathrm e^xdd x frac_^ fracydd y tcbhighmathloesungtfracln!bigl+mathrm e^xbigr+c %q abc Fx tcbhighmathaufgabe tanxsec^xdd x substitutiony:tan xquad dd ysec^ xdd x ydd y tcbhighmathloesungtfractan^x+c %r abc Fx tcbhighmathaufgabe fracsqrtx-dd x substitutiony:x-quad dd ydd x frac y^-fracdd y tcbhighmathloesungtfracsqrtx-+c %s abc Fx tcbhighmathaufgabe_^ xsqrt+x^dd x substitutiony:+x^quad dd yxdd x frac_^ y^fracdd y tcbhighmathloesungtfrac+x^^/+c %t abc Fx tcbhighmathaufgabe fracx^x^+^dd x substitutiony:x^+quad dd yx^dd x frac y^-dd y tcbhighmathloesung-fracx^++c %u abc Fx tcbhighmathaufgabe fracsqrt-xdd x substitutiony:-xquad dd y-dd x -frac y^-fracdd y tcbhighmathloesung-sqrt-x+c %v abc Fx tcbhighmathaufgabe_^ fracxsqrtx^+dd x substitutiony:x^+quad dd yxdd x frac_^ y^-fracdd y tcbhighmathloesungtfracsqrtx^++c abc Fx tcbhighmathaufgabe frac+x+^dd x substitutiony:x+quad dd ydd x frac frac+y^dd y tcbhighmathloesungtfracarctanx++c %x abc Fx tcbhighmathaufgabe_^fracln fracmathrm e^xmathrm e^x+dd x substitutiony:mathrm e^x+quad dd ymathrm e^xdd x frac_^ fracydd y tcbhighmathloesungtfracln!biglmathrm e^x+bigr+c abclist