Lösungen/Solutions/E1S1AnUe/Ex11

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

Ueb/Ex 1      W

a

f1[x_] := Sin[1/x]

D[f1[x], x]

b

D[Sin[x]/x, x]

c

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

d

D[Sin[ϖ x^2  +  φ], x]

e

D[E^x /Log[x], x]

f

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

g

D[Cosh[x] Sinh[x], x]

h

D[1/Sinh[x], x]

?Csch

i

D[3 x^3 - 2  x^2 - 5, x]

k

D[Sin[x]^3 + Sin[x]^2 + Sin[x] + 1, x]

Ueb/Ex 2      W

a

Plot[
        Evaluate[D[Cosh[x] Sinh[x], x]], {x, -1.3, 1.3}];

Solve[Evaluate[D[Cosh[x] Sinh[x], x]] == 4, {x}]

% // N

b

Solve[Evaluate[D[Sin[x], x]] == 1/2, {x}]

Ueb/Ex 3      W

Plot[{E^x, E^(-x) + 2}, {x, -1.3, 1.3}];

FullSimplify[E^x == E^(-x) + 2]

red = Reduce[E^x == E^(-x) + 2]

ToRules[red]

x0 = Log[1 + (Sqrt[2])];

α1 = 
      Evaluate[D[E^x, x]] /.  x -> x0  //  ArcTan

N[α1]

α2 = 
      Evaluate[D[E^(-x) + 2, x]] /.  x -> x0  //  
        ArcTan

N[α2]

α1 + α2

% // N