Réponse :

Bonjour

Exercice 5

1) F(x) = x² + 1/x²

F'(x) = 2x - 2x/x² = 2x - 2/x³ = (2x⁴ - 2)/x³ = 2(x⁴ - 1)/x³ = f(x)

2) F(x) = x - ln(1 + )

F'(x) = 1 - /(1 + ) = (1 + )/(1 + ) = 1/(1 + ) = f(x)

3) F(x) = ln(lnx)

F'(x) = (1/x)/lnx = 1/xlnx = f(x)

4) F(x) = x cosx

F'(x) = 1×cosx + x(-sinx) = cosx - x sinx = f(x)

Exercice 7

1) f(x) = x⁴ - 4x³ + x² - 4x + 3

F(x) = x⁵/5 - x⁴ + x³/3 - 2x² + 3x

2) f(x) = (x² - 2x + 1)/3

F(x) = (x³/3 - x² +x)/3

3) f(x) = 1 - 1/x³

F(x) = x + 1/(2x²)

4) f(x) = -1/x³ + 4/x² - 1

F(x) = 1/(2x²) - 4/x - x

5) f(x) = 4/x + 2

F(x) = 4ln(x) + 2