Find and simplify the coefficient of \(x^7\) in the binomial expansion of \(\left( x^2 + \dfrac{2}{x} \right)^8\).

Calculate the minimum value of \(x^2 + \dfrac{2}{x}\) for positive values of \(x\).

Given that \(y = \left( x^2 + \dfrac{2}{x} \right)^8\), find the value of \(\dfrac{dy}{dx}\) when \(x = -1\).