Question

Derivada primeira de f (x): 1-x/x+3

Answer 1

Resposta:

-4/(x+3)²

Explicação passo-a-passo:

Regra do quociente

$f (x)=\frac{1-x}{x+3}\\g(x)=1-x\\g'(x)=-1\\h(x)=x+3\\h'(x)=1$

$\frac{g(x)}{h(x)}=\frac{g'(x)*h(x)-g(x)*h'(x)}{(h(x))^2}\\\frac{g(x)}{h(x)}=\frac{(-1)*(x+3)-(1-x)*1}{(x+3)^2}\\\frac{g(x)}{h(x)}=\frac{-x-3-1+x}{(x+3)^2}=\frac{-4}{(x+3)^2}$