Exercices de dérivation

Dériver les fonctions suivantes

Clear[f]; i = 1;
a = 
        Random[Integer, {-5, 5}];
b = 
        Random[Integer, {-5, 5}];
c = 
        Random[Integer, {-5, 5}];
d = 
        Random[Integer, {-5, 5}];
e = Random[Integer, {-5, 5}]; 
    g = Random[Integer, {-5, 5}];
f[x] := 
        Sqrt[a + Abs[b]*x]/(Abs[c] x + d);
sol[1] = 
        Simplify[D[f[x], x]];
Print[i, ")  f(x) = ", f[x]];

Clear[f]; i = i + 1;
a = 
        Random[Integer, {-5, 5}];
b = 
        Random[Integer, {-5, 5}];
c = 
        Random[Integer, {-5, 5}];
f[x] := 
        Sqrt[Abs[a]*x^2 + b*x + c];
sol[i] = 
        Simplify[D[f[x], x]];
Print[i, ")  f(x) = ", f[x]];

Clear[f]; i = i + 1;
a = 
        Random[Integer, {-5, 5}];
b = 
        Random[Integer, {-5, 5}];
c = Random[Integer, {-5, 5}]; 
    d = Random[Integer, {-5, 5}]; 
    f[x] := Sqrt[Abs[a]*x + b]/(x^2 + c);
sol[i] := 
        Simplify[D[f[x], x]];
Print[i, ")  f(x) = ", f[x]];

Clear[f]; i = i + 1;
a = 
        Random[Integer, {-5, 5}];
b = 
        Random[Integer, {-5, 5}];
c = 
        Random[Integer, {-5, 5}];
f[x] := (x^2 + c)/
          Sqrt[Abs[a]*x + b];
sol[i] = 
        Simplify[D[f[x], x]];
Print[i, ")  f(x) = ", f[x]];

Clear[f]; i = i + 1;
a = 
        Random[Integer, {-5, 5}];
b = 
        Random[Integer, {-5, 5}];
c = Random[Integer, {-5, 5}]; 
    d = Random[Integer, {-5, 5}];
f[x] := 
        Sqrt[(Abs[a]*x + b)/(c*x + 
                Abs[d])];
sol[i] = 
        Simplify[D[f[x], x]];
Print[i, ")  f(x) = ", f[x]];

Clear[f]; i = i + 1;
a = Random[Integer, {-5, 5}]; 
    b = Random[Integer, {-5, 5}];
c = Random[Integer, {-5, 5}]; 
    d = Random[Integer, {-5, 5}];
f[x] := (Abs[a]*x + b)^
          c;
sol[i] = 
        Simplify[D[f[x], x]];
Print[i, ")  f(x) = ", f[x]];

Clear[f]; i = i + 1;
a = 
        Random[Integer, {-5, 5}];
b = 
        Random[Integer, {-5, 5}];
c = Random[Integer, {-5, 5}]; 
    d = Random[Integer, {-5, 5}];
f[
          x] := ((Abs[a]*x^2 + b*x + c)^(1/3));
sol[i] = 
        Simplify[D[f[x], x]];
Print[i, ")  f(x) = ", f[x]];

Clear[f]; i = i + 1;
a = 
        Random[Integer, {-5, 5}];
b = 
        Random[Integer, {-5, 5}];
c = Random[Integer, {-5, 5}]; 
    d = Random[Integer, {-5, 5}];
f[x] := 
        Sqrt[Abs[a] *x^2  +  b x + c ]/(Abs[c] x + 
              d);
sol[i] = 
        Simplify[D[f[x], x]];
Print[i, ")  f(x) = ", f[x]];

Clear[f]; i = i + 1;
a = 
        Random[Integer, {-5, 5}];
b = 
        Random[Integer, {-5, 5}];
c = Random[Integer, {-5, 5}]; 
    d = Random[Integer, {-5, 5}];
f[x] := 
        Abs[a]*x/Sqrt[Abs[b]*x^2 + c];
sol[i] = 
        Simplify[D[f[x], x]];
Print[i, ")  f(x) = ", f[x]];

Clear[f]; i = i + 1;
a = 
        Random[Integer, {-5, 5}];
b = 
        Random[Integer, {-5, 5}];
c = Random[Integer, {-5, 5}]; 
    d = Random[Integer, {-5, 5}];
f[x] := 
        Sqrt[a*x + b]/Sqrt[c + d*x];
sol[i] = 
        Simplify[D[f[x], x]];
Print[i, ")  f(x) = ", f[x]];

Solutions :

Do[Print[i, ") f'(x) = ", sol[i]], {i, 1, 10}]