Lösungen/ Solutions

1

f[x_] :=  x^3 - 6  x^2 + 12  x - 8

Plot[f[x], {x, -1, 3}];

D[f[x], {x, 1}]

Solve[12 - 12 x + 3 (x^2) == 0, {x}]

WP

Keinen weiteren Schnittpunkt

2

f[x_] :=  (x + 1)^3

Plot[f[x], {x, -2, 0}];

D[f[x], {x, 1}]

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

ArcTan[12] // N

ArcTan[12]/ Degree  // N

Solve[3 (((1 + x))^2) == 12, {x}]

3

g[x_] :=  16  x^4 + 8  x^3 + 4  x^2 + 2  x + 1; h[x_] := 5

f[x_] :=  g[x] h[x] + 1

D[f[x], {x, 1}]

D[f[x], {x, 1}] // Expand

4

f[x_] :=  (E^x + E^(-x))/2;  
    g[x_] :=  (E^x - E^(-x))/2

D[f[x], {x, 1}]

Solve[
      (1/2) (-(E^(-x)) + (E^x)) == 
        0, {x}]

D[g[x], {x, 1}]

5

f[x_] :=  E^x Sin[x] - 4; D[f[x], {x, 1}]

g[x_] :=  Sin[x]/(E^x  - 4); D[g[x], {x, 1}]

Together[%]

6

f[x_] :=  Log[Sin[x]]; D[f[x], {x, 1}]

f[x_] :=  E^(x^c); D[f[x], {x, 1}]

7

f[x_] :=  a Cos[x - Pi/2];  f[x]

D[f[x], {x, 1}]

D[f[x], {x, 1}] /. x -> 0

Solve[a == Tan[Pi/6], {a}]

N[%]