Question

Encontre a derivada da função y=(x²+1/x²-1)³

Answer 1

$y = \left(\dfrac{x^2+1}{x^2-1}\right)^3 \Longrightarrow \\\\\\\ y' = 3 \cdot \left(\dfrac{x^2+1}{x^2-1}\right)^2\cdot \left(\dfrac{x^2+1}{x^2-1}\right)' \Longleftrightarrow \\\\\\y' = 3 \cdot \left(\dfrac{x^2+1}{x^2-1}\right)^2\cdot \left[\dfrac{2x \cdot (x^2-1) - 2x \cdot (x^2 + 1)}{(x^2-1)^2}\right] \Longleftrightarrow \\\\\\y' = 3 \cdot \dfrac{( x^2+1)^2}{(x^2-1)^4}\cdot -4x \Longleftrightarrow \\\\\\\boxed{y' = -12x \cdot \dfrac{( x^2+1)^2}{(x^2-1)^4}}$