Question

Calcular a derivada da função,
$y = \frac{x}{x+1}$

Answer 1

y=x/(x+1)

Seja f(x)=x e g(x)=x+1.Temos que:

dy/dx=(f'*g-g'*f)/g²

dy/dx=(1*x+1-1*x)/(x+1)² ⇒ dy/dx=(x+1-x)/(x+1)² ⇒ dy/dx=1/(x+1)²