Exercices de dérivation de fonctions composées

Dériver les fonctions suivantes

1")  f(x) = "(Sqrt[5 (x^2)-3 x+2])

2")  f(x) = "(((8-5 (x^2)))^2)

3")  f(x) = "(1/(((3 x-1))^3))

4")  f(x) = "sin(1-2 (x^2))

5")  f(x) = "(sin^3)(x)

6")  f(x) = "cos((Sqrt[x]))

7")  f(x) = "sin((1/x))

8")  f(x) = "cos(3 x) sin(x)

9")  f(x) = "sin((x/(x-2)))

10")  f(x) = "4 cos(3 x)-sin(x)

Solutions :

1) f'(x)=((10 x-3)/(2 (Sqrt[5 (x^2)-3 x+2])))

2) f'(x)=20 x (5 (x^2)-8)

3) f(x)=-(9/(((3 x-1))^4))

4) f'(x)=-4 x cos(1-2 (x^2))

5) f'(x)=3 (sin^2)(x) cos(x)

6) f'(x)=-((sin((Sqrt[x])))/(2 (Sqrt[x])))

7) f'(x)=-((cos((1/x)))/(x^2))

8) f'(x)=cos(x) cos(3 x)-3 sin(x) sin(3 x)

9) f'(x)=-((2 cos((x/(x-2))))/(((x-2))^2))

10) f'(x)=-12 sin(3 x)-cos(x)  
*modifié 10-09-14