Question

qual a derivada? F(x)= x ln (3x+1)

Answer 1

$f(x)=x\cdot\ln(3x+1)$ aplicando a regra do produto temos

$f'(x)=x'\cdot\ln(3x+1)+x\cdot\overbrace{(\ln(3x+1))'}^{\mbox{regra da cadeia}}\\\\f'(x)=\ln(3x+1)+x\cdot\dfrac{1}{3x+1}\cdot(3x+1)'\\\\\boxed{\boxed{f'(x)=\ln(3x+1)+\dfrac{3x}{3x+1}}}$