Réponse :
f : x → 9/x² x ≠ 0
calculer et simplifier l'expression
(f(x0+h) - f(x0))/h = (9/(x0+h)² - 9/x²0)/h
f(x0+h) = 9/(x0+h)² =
f(x0) = 9/x²0
(f(x0+h) - f(x0))/h = (9/(x0+h)² - 9/x²0)/h
= 9 x²0/x²0(x0+h)²)/h - 9(x0+h)²/x²0(x0+h)²/h
= (9 x²0 - 9 x²0 - 18 x0h + 9 h²)/x²0(x0+h)²/h
= h(9 h - 18 x0)/hx²0(x0+h)²
= (9 h - 18 x²0)/x²0(x0+h)²
= 9 h/x²0(x0+h)²] - 18/(x0+h)²
Explications étape par étape :
