Exercices de dérivation 3

Dériver les fonctions suivantes

Clear[f];i=1;
a=Random[Integer,{-5,5}];
b=Random[Integer,{-5,5}];
c=Random[Integer,{-5,5}];
f[x]:=(a x+b)/(x^2+c);
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]:=( x+a)^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}];
f[x]:=(a x+b)/Sqrt(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+a) Sqrt[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}];
f[x]:= (a+b Sqrt[x])/(b + c Sqrt[x]);
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]:=(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[(a x + b)/(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]:=(a Sin[x] + b Cos[x])/(c Sin[x]+d Cos[x]);
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]:=Sin[(a x+b)/(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}];
f[x]:=c Sin[a x] + d Cos[b 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}]