Question

x^2+x+1 derivar por formula general​

Answer 1

Respuesta:

f'(x) = 2x + 1

Explicación:

x² + x + 1

f(x) = x² + x + 1

f'(x) = lim→0  (f(x + h) - f(x)) / h

f(x + h) = (x + h)² + (x + h) + 1

(f(x + h) - f(x)) / h = ((x + h)² + (x + h) + 1 - (x² + x + 1)) / h

((x + h)² + (x + h) + 1 - (x² + x + 1)) / h

(x² + 2xh + h² + x + h + 1 - x² - x - 1) / h

(2xh + h² + h) / h

h(2x + h + 1) / h

2x + h + 1

f'(x) = lim→0  (2x + h + 1)

f'(x) = (2x + 0 + 1)

f'(x) = 2x + 1