Exercise:
Differentiate the following polynomials with respect to x. nprvmulticols abclist abc fx x abc fx x^ abc fx x^ abc fx x^ abc fx x^ + x^ abc fx x^ - x^ abc fx -x^ + x abc fx x^ - x^ + x^ abc fx x^ + x^ + x + abc fx x^ - x^ + x^ - x^ + x abc fx x^ + x^ - x^ + abc fx xx^ + abc fx x^ + xx - abc fx x^x^ - x + abc fx x^ - xx^ + abc fx x^x - x + abc fx x^ + ^ abc fx x^ - x + ^ abc fx x^ + x^ + x + ^ abc fx x^ - x^x + abc fx xx - x + x^ + abc fx x^ - x^x^ + abc fx x^ + ^x^ - x + abc fx x^ + x + ^x^ + x + ^ abclist nprvmulticols

Solution:
abclist %a abc f'x %b abc f'x x %c abc f'x x^ %d abc f'x x^ %e abc f'x x^ + x^ %f abc f'x x^ - x %g abc f'x -x^ + %h abc f'x x^ - x^ + x %i abc f'x x^ + x + %j abc f'x x^ - x^ + x^ - x + %k abc f'x x^ + x^ - x^ %l abc Either product rule fg' f'g+fg' which leads to f'x x^+ + x x x^+ + x^ x^+ or expanding terms fxxx^+ x^+x what obviously also leads to this result. %m abc Product rule fg' f'g+fg' leads to: f'x x + x - + x^ + x x + x - + x^ + x x^+x- %n abc Product rule fg' f'g+fg' leads to: f'x xx^ - x + + x^x - x^ - x^ + x %o abc Produktregel fg' f'g+fg' führt auf: f'x x^ - x^ + + x^ - xx x^ + x^ - %p abc Use product rule on three functions uvw' u'vw + uv'w + uvw' or expand the function to fx x^ + x^ - x^ either way: f'x x^x - x + + x^x + + x^x - x^ + x^ - x^ %q abc Use chain rule fg' f'g g': f'x x^ + x xx^ + x^ + x %r abc Use chain rule fcirc g' f' circ g g': f'x x^ - x + ^ x - %s abc Chain rule: f'x x^ + x^ + x + x^ + x + %t abc Product rule: f'x x^ - xx - x + + x^ - x^ x^ - x^ + x %u abc Product rule with multiple functions or expand to fx x^ + x^ - x^ + x^ - x then: f'x x^ + x^ -x^ +x - %v abc Product rule: f'x x^ - xx^ - x^ + + x^ - x^x x^ - x^ - x^ + x %w abc Product rule: f'x xx^ + x^ - x + + x^ + ^x^ - %x abc Product + chain rule. abclist