Question

a derivada da função y=x³ /3x 1é?

Answer 1

Usando a regra do quociente: 

$y= \frac{u}{v}\ \ \ \ -\ \textgreater \ \ \ \ y'= \frac{u'.v-u.v'}{v^2}$

$y= \frac{x^3}{3x+1} \\ \\ y'= \frac{(x^3)'(3x+1)-(x^3)(3x+1)'}{(3x+1)^2} \\ \\ y'= \frac{3x^2(3x+1)-x^3.(3)}{(3x+1)^2} \\ \\ y'= \frac{9x^3+3x^2-3x^3}{(3x+1)^2} \\ \\ y'= \frac{6x^3+3x^2}{(3x+1)^2} \\ \\ \boxed{y'= \frac{3x^2(2x+1)}{(3x+1)^2}}$

Espero que goste . Comenta Depois :)