Lösungen

1

a

f[x_]:= 5x^4-2x^3+5-8x^(-2)+4;
D[f[x],x]

b

f[x_]:= Log[x] Sin[x];
D[f[x],x]

c

f[x_]:= x^2/(3 Cos[x]);
D[f[x],x]

d

f[x_]:= Sin[5x^3+4x^2-6];
D[f[x],x]

2

a

f[x_]:= E^x+1;
ArcTan[D[f[x],x]]/.x->2

%//N

%/Degree//N

b

f[x_]:= Cos[3x];
ArcTan[D[f[x],x]]/.x->2

%//N

%/Degree//N

3

f[x_]:= x(x-4)(x+5); f[x]//Expand

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

Plot[f[x],{x,-5,4}]

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

%//N

4

f[x_]:= Cos[x]/4+4;
Solve[D[f[x],x]==2/11,{x}]

%//N

Plot[f[x],{x,0,2Pi}]

-0.81434+2Pi

5

a

f[x_]:= 4(x-2)(x+2);
Integrate[f[x],{x,-2,2}]

N[%]

b

f[x_]:= 3/x^6;
Integrate[f[x],{x,1,Infinity}]

N[%]

6

f[x_]:= 3 E^x;
Integrate[f[x],{x,1,x2}]

Solve[Evaluate[Integrate[f[x],{x,1,x2}]]==4,{x2}]

%//N