Question

1. Usando as regras de derivação,encontre a derivada das seguintes funções:

1.) y=x
___
x²+1

Answer 1

$y=\dfrac{x}{x^2+1}$


Derive usando a regra do quociente:

$y'=\left(\dfrac{x}{x^2+1} \right )'\\\\\\ y'=\dfrac{(x)'\cdot (x^2+1)-x\cdot (x^2+1)'}{(x^2+1)^2}\\\\\\ y'=\dfrac{1\cdot (x^2+1)-x\cdot 2x}{(x^2+1)^2}\\\\\\ y'=\dfrac{x^2+1-2x^2}{(x^2+1)^2}\\\\\\\\ \therefore~~\boxed{\begin{array}{c}y'=\dfrac{1-x^2}{(x+1)^2} \end{array}}$


Bons estudos! :-)