Question

Encontre f’(x) a partir de f(x)=$\sqrt[3]{(x^2 + 1)^2}$

Answer 1

Resposta:

f'(x) = (4x)/[3∛(x²+1)]

Explicação passo-a-passo:

f(x) =(x²+1)^(2/3)

v = x²+1

v' = 2x

k = v^(2/3)

k' = (2/3)v^(2/3 -1)

k' = (2/3)v^(-1/3)

f'(x) = v'.k'

f'(x) = 2x.(2/3)v^(-1/3)

f'(x) = (4x/3)v^(-1/3)

f'(x) = (4x/3)[x²+1)^(-1/3)

f'(x) = (4x)/[3∛(x²+1)]