Exercices de dérivation 4

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]:=a*x^Abs[d]-2x^Abs[b]+c*Sqrt[x]-d/x^Abs[e]+g;
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^Abs[a]+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]:=(a x+b)^2/(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}];
f[x]:=Cos[x]^Abs[a]*Tan[x]^Abs[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]:= (a+b *x)/(d + c*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 +b x)*(c*x+d/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]:=((x^(1/3))+1)/(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 *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*Cos[ x]/(Sin[ 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*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}]

3) f'(x)=(((2 x+1) (2 x+3))/(5 (((x+1))^2)))