Lösungen/ Solutions

1

f[x_] := 1/3 x^3 - 4  x^2 + 2  x - 1

Plot[f[x], {x, -4, 12}];

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

Solve[2 - 8 x + (x^2) == 0, {x}]

Solve[2 - 8 x + (x^2) == 0, {x}] // N

ArcTan[2 - 8 x + (x^2)] /. x->4

-ArcTan[14]

-ArcTan[14] // N

ArcTan[14] /(2  Pi) 360 // N

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

Plot[2 - 8 x + (x^2), {x, -4, 12}];

ArcTan[-8 + 2 x] /. x->4

2

D[x^2 (4  x  - 3), {x, 1}] // Expand

D[x^2 (4  x  - 3), {x, 2}] // Expand

D[x^2 (4  x  - 3), {x, 3}] // Expand

D[x^2 (4  x  - 3), {x, 4}] // Expand

3

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

D[x^2 Log[x], {x, 1}] // Expand

D[x^2  E^x, {x, 1}] // Expand

D[Sin[x] Cos[x], {x, 1}] // Expand

4

D[(x + 1)/x^2, {x, 1}] // Expand

D[Log[2  x + 3], {x, 1}] // Expand

D[Cos[2  x + 3], {x, 1}] // Expand

D[Cos[x^4], {x, 1}] // Expand