Lösungen/Solutions/E1S1AnUe/Ex10

L = 
      Lektion/Leçon-- Sprechstunde/
          heures de consultation
W = Work/Arbeit/Travail
A   = Anhang/  Annexe / Appendice

Ueb/Ex 1      W

a

f[x_, 1] := x^3 + 4  x^2 - x + 5;
f[x_, 2] := 2 x^5 + 7  x^3 + 3  x - 8;

f[x_, 3] := 
        f[x, 1]  f[x, 2] // Expand;
 f[x_, 4] := f[x, 1]  +  f[x, 2];
{f[x, 3], f[x, 4]}

Table[{f[x, k], D[f[x, k], x]}, {k, 1, 4}]

b

D[Cos[x]^3, x]

D[Cos[x]^n, x]

D[x^2 Cos[x], x]

c

D[Cos[x]/x^2, x]

D[1/Cos[x], x]

D[(x^2 + Cos[x])/(x Sin (x)), x]

d

D[Sin[Cos[x]], x]

D[Sin[Cos[x]^2], x]

D[Sin[3 x^2 + 4  x - 5], x]

D[Sin[1/(x^2 - 2  x + 3)], x]

Ueb/Ex 2      W

a

f[x_] := x^3 + 4  x^2 - x + 5;
g[x_] := 2 x^5 + 7  x^3 + 3  x - 8;

D[f[x], x]

D[f[x], x] /.  x -> 1

ArcTan[D[f[x], x] /.  x -> 1]

ArcTan[D[f[x], x] /.  x -> 1] // N

D[g[x], x]

D[g[x], x] /.  x -> 1

ArcTan[D[g[x], x] /.  x -> 1]

ArcTan[D[g[x], x] /.  x -> 1] // N

b

f[x_] := x^3 + 4  x^2 - x + 5;

Solve[D[f[x], x] == 2, {x}]

c

g[x_] := a x^3 + 4  x^2 - x + 5;

Solve[D[g[x], x] == 2 /. x -> 1, {a}]