(%i1) Hinweis: sqrt = square root = Wurzel 

(%i2) S. 90, Nr. 8

(%i3) a)

(%i4) f(x) := (2*x^2 - 1) * sqrt(x^2 - 1);
                                    2            2
(%o4)                   f(x) := (2 x  - 1) sqrt(x  - 1)

(%i5) diff(f(x),x);
                                                 2
                                  2        x (2 x  - 1)
(%o5)                   4 x sqrt(x  - 1) + ------------
                                                 2
                                           sqrt(x  - 1)

(%i6) b)

(%i7) g(x) := sqrt(x * sqrt(x));
(%o7)                       g(x) := sqrt(x sqrt(x))

(%i8) diff(g(x),x);
                                  3 sqrt(x)
(%o8)                            ------------
                                         3/2
                                 4 sqrt(x   )

(%i9) c)

(%i10) h(x) := (x^3 - 1)^4 * (sqrt(x) + x)^2;
                                 3     4              2
(%o10)                 h(x) := (x  - 1)  (sqrt(x) + x)

(%i11) diff(h(x),x);
              1                          3     4
(%o11) 2 (--------- + 1) (x + sqrt(x)) (x  - 1)
          2 sqrt(x)
                                                     2              2   3     3
                                               + 12 x  (x + sqrt(x))  (x  - 1)

(%i12) d)

(%i13) m(x) := (x^2 + sqrt(x^3)) * (sqrt(2*x));
                                 2         3
(%o13)                 m(x) := (x  + sqrt(x )) sqrt(2 x)

(%i14) diff(m(x),x);
                    3     2                           2
              sqrt(x ) + x                         3 x
(%o14)       --------------- + sqrt(2) sqrt(x) (---------- + 2 x)
             sqrt(2) sqrt(x)                            3
                                                2 sqrt(x )