Question

Obtenha a derivada da função:
f(x)= ∜(1+2x+x³)

Answer 1

Resposta:

f(x)= ∜(1+2x+x³)

Regra da cadeia

u=1+2x+x³

f(x)= ∜u  =u^(1/4)

d[f(x)]/dx = u' * [u^(1/4)]'

u'  =(1+2x+x³)' = 0 +2 +3x²

[u^(1/4)]' = (1/4) * u^(1/4-1) =(1/4)*u^(-3/4)  <<<===regra do tombo

d[f(x)]/dx =(2+3x²) * (1/4)*u^(-3/4)

como u= 1+2x+x³ , ficamos com:

d[f(x)]/dx =(2+3x²) * (1/4) * 1/(1+2x+x³)^(3/4)

d[f(x)]/dx = (2+3x²) * /4∜(1+2x+x³)³