Question

Calcule a derivada a seguir:
 y= 3x²-5x+8
         7

Answer 1

Regra do quociente

$\frac{d}{dx} ( \frac{f(x)}{g(x)} )= \frac{g(x)*f'(x)-f(x)*g'(x)}{[g(x)]^2}$

fazendo 

f(x)=3x^2-5x+8     f'(x)=6x-5
g(x)=7                    g'(x)=0

$y'= \frac{7*(6x-5)-(3x^2-5x+8)*0}{7^2}$

$y'= \frac{42x-35}{49}$

$\boxed{y'= \frac{6x-5}{7} }$