Exercise:
nprvmulticols prvmulticols abclist %a abc displaystyle fracx^ + x + ddx %b abc displaystyle fracx^ - x + ddx %c abc displaystyle fracx^ + x - ddx %d abc displaystyle fracx^ - x + ddx %e abc displaystyle fracx^ + x + ddx %f abc displaystyle fracx^ + x + ddx %g abc displaystyle fracx^ - x + ddx %h abc displaystyle fracx^ + x + ddx %i abc displaystyle fracx^ - x + ddx %j abc displaystyle fracx^ + x + ddx %k abc displaystyle fracx^ + x + ddx %l abc displaystyle fracx^ - x + ddx abclist multicols

Solution:
abclist % a abc Fx tcbhighmathaufgabe fracx^+x+ddx fracx^+fracx+fracddx fracleftx+fracright^-fracddx substitutiony:x+frac quad ddxddy fracfrac fracy^-ddy fracy^-ddy substitutionz:y quad ddyfracddz - frac-z^ddz - operatornameartanhz + c - operatornameartanhy + c operatornameartanh-y + c tcbhighmathloesung- operatornameartanhx+ + c % b abc Fx tcbhighmathaufgabe fracx^-x+ddx fracleftx^-fracx+fracrightddx fracleftleftx-fracright^+fracrightddx substitutiony:x-frac quad ddxddy fraclefty^+fracrightddy fracfracfracy^+ddy substitutionz:fracsqrty quad ddyfracsqrtddz fracfracz^+fracsqrtddz fracsqrtfrac+z^ddz fracsqrtarctanz+c fracsqrtarctan!leftfracsqrtyright+c fracsqrtarctan!leftfracsqrtleftx-fracrightright+c tcbhighmathloesungfracsqrtarctan!leftfracx-sqrtright+c % c abc Fx tcbhighmathaufgabe fracx^ + x - ddx fracleftx^+fracx-fracrightddx fracleftleftx+fracright^-fracrightddx substitutiony:x+frac quad ddxddy fraclefty^-fracrightddy -fracfracfrac-y^ddy - fracfrac-fracy^ddy substitutionz:fracsqrty quad ddyfracsqrtddz - fracfrac-z^fracsqrtddz -fracsqrt frac-z^ddz -fracsqrtoperatornameartanhz+c -fracsqrtoperatornameartanh!leftfracsqrtyright+c -fracsqrtoperatornameartanh!leftfracx+sqrtright+c tcbhighmathloesung-fracsqrtoperatornameartanh!leftfracx+sqrtright+c % d abc Fx tcbhighmathaufgabe fracx^ - x + ddx fracleftx^-fracx+fracrightddx fracleftleftx-fracright^+fracrightddx substitutiony:x-frac quad ddxddy fraclefty^+fracrightddy fracfracfracy^+ddy substitutionz:fracsqrty quad ddyfracsqrtddz fracfracz^+fracsqrtddz fracsqrt frac+z^ddz fracsqrtarctanz+c fracsqrtarctan!leftfracsqrtyright+c fracsqrtarctan!leftfracx-sqrtright+c tcbhighmathloesungfracsqrtarctan!leftfracx-sqrtright+c % e abc Fx tcbhighmathaufgabe fracx^ + x + ddx fracleftx^+fracx+fracrightddx fracleftleftx+fracright^+fracrightddx substitutiony:x+frac quad ddxddy fraclefty^+fracrightddy fracfracfracy^+ddy substitutionz:fracsqrty quad ddyfracsqrtddz fracfracz^+fracsqrtddz fracsqrt frac+z^ddz fracsqrtarctanz+c fracsqrtarctan!leftfracsqrtyright+c fracsqrtarctan!leftfracx+sqrtright+c tcbhighmathloesungfracsqrtarctan!leftfracx+sqrtright+c % f abc Fx tcbhighmathaufgabe fracx^ + x + ddx fracx^+x+ddx fracleftx+right^+ddx substitutiony:x+ quad ddxddy fracy^+ddy substitutionz:y quad ddyddz frac+z^ddz arctanz+c arctany+c arctanx++c tcbhighmathloesungarctanx++c % g abc Fx tcbhighmathaufgabe fracx^ - x + ddx fracleftx^-x+fracrightddx fracleftleftx-right^+fracrightddx substitutiony:x- quad ddxddy fraclefty^+fracrightddy fracfracfracy^+ddy substitutionz:sqrtfracy fracsqrty quad ddysqrtfracddzfracsqrtddz fracfracz^+fracsqrtddz fracsqrt frac+z^ddz fracsqrtarctanz+c fracsqrtarctan!leftfracsqrtyright+c fracsqrtarctan!leftfracsqrtx-right+c tcbhighmathloesungfracsqrtarctan!leftfracsqrtx-right+c % h abc Fx tcbhighmathaufgabe fracx^ + x + ddx fracx^+x+ddx fracleftx+right^+ddx substitutiony:x+ quad ddxddy fracy^+ddy substitutionz:y quad ddyddz frac+z^ddz arctanz+c arctany+c arctanx++c tcbhighmathloesungarctanx++c % i abc Fx tcbhighmathaufgabe fracx^ - x + ddx fracleftx^-x+fracrightddx fracleftleftx-fracright^+fracrightddx substitutiony:x-frac quad ddxddy fraclefty^+fracrightddy fracfracy^+ddy substitutionz:sqrty quad ddyfracsqrtddz fracfracz^+fracsqrtddz fracsqrt frac+z^ddz fracsqrtarctanz+c fracsqrtarctan!leftsqrtyright+c fracsqrtarctan!leftsqrtleftx-fracrightright+c tcbhighmathloesungfracsqrtarctan!leftsqrtleftx-fracrightright+c % j abc Fx tcbhighmathaufgabe fracx^ + x + ddx fracleftx^+x+fracrightddx fracleftleftx+fracright^+fracrightddx substitutiony:x+frac quad ddxddy fraclefty^+fracrightddy fracfracfracy^+ddy substitutionz:sqrtfracy fracsqrty quad ddysqrtfracddzfracsqrtddz fracfracz^+fracsqrtddz fracsqrt frac+z^ddz fracsqrtarctanz+c fracsqrtarctan!leftfracsqrtyright+c fracsqrtarctan!leftfracsqrtleftx+fracrightright+c tcbhighmathloesungfracsqrtarctan!leftfracsqrtleftx+fracrightright+c % k abc Fx tcbhighmathaufgabe fracx^ + x + ddx fracleftx^+fracx+rightddx fracleftleftx+fracright^+fracrightddx substitutiony:x+frac quad ddxddy fraclefty^+fracrightddy fracfracfracy^+ddy substitutionz:fracsqrty quad ddyfracsqrtddz fracfracz^+fracsqrtddz fracsqrt frac+z^ddz fracsqrtarctanz+c fracsqrtarctan!leftfracsqrtyright+c fracsqrtarctan!leftfracx+sqrtright+c tcbhighmathloesungfracsqrtarctan!leftfracx+sqrtright+c % l abc Fx tcbhighmathaufgabe fracx^ - x + ddx fracleftx^-x+fracrightddx fracleftleftx-fracright^+fracrightddx substitutiony:x-frac quad ddxddy fraclefty^+fracrightddy fracfracfracy^+ddy substitutionz:sqrtfracy fracsqrty quad ddysqrtfracddzfracsqrtddz fracfracz^+fracsqrtddz fracsqrt frac+z^ddz fracsqrtarctanz+c fracsqrtarctan!leftfracsqrtyright+c fracsqrtarctan!leftfracsqrtleftx-fracrightright+c tcbhighmathloesungfracsqrtarctan!leftfracsqrtleftx-fracrightright+c abclist