Lösungen

1

a

f[x_]:= 4x^3-3x+5-6x^(-1);
D[f[x],x]

b

f[x_]:= E^x Cos[x];
D[f[x],x]

c

f[x_]:= x^3/Sin[x];
D[f[x],x]

d

f[x_]:= Cos[2x^3+3x];
D[f[x],x]

2

a

f[x_]:= Log[x];
ArcTan[D[f[x],x]]/.x->2

%/Degree//N

b

f[x_]:= Sin[2x];
ArcTan[D[f[x],x]]/.x->2

%/Degree//N

3

f[x_]:= x(x-2)(x+3); f[x]//Expand

D[f[x],x]//Expand

Solve[D[f[x],x]==0,{x}]

%//N

4

f[x_]:= Sin[x]/2;
Solve[D[f[x],x]==1/5,{x}]

%//N

5

a

f[x_]:= (x-1)(x+1);
Integrate[f[x],{x,-1,1}]

b

f[x_]:= 1/x^4;
Integrate[f[x],{x,1,Infinity}]

6

f[x_]:= E^x;
Integrate[f[x],{x,0,x2}]

Solve[Evaluate[Integrate[f[x],{x,0,x2}]]==2,{x2}]

%//N