First, simplify the expression \(\frac{2x^3 + 5}{x}\) by dividing each term in the numerator by \(x\):

\(y = \frac{2x^3}{x} + \frac{5}{x} = 2x^2 + \frac{5}{x}\).

Now, differentiate each term separately:

The derivative of \(2x^2\) is \(4x\).

The derivative of \(\frac{5}{x}\) is \(-\frac{5}{x^2}\) or equivalently \(-5x^{-2}\).

Therefore, the derivative \(\frac{d}{dx}\) is:

\(4x - \frac{5}{x^2}\) or \(4x - 5x^{-2}\).

To differentiate \(4x + \frac{6}{x^2}\), we first rewrite \(\frac{6}{x^2}\) as \(6x^{-2}\).

The derivative of \(4x\) with respect to \(x\) is 4.

The derivative of \(6x^{-2}\) with respect to \(x\) is found using the power rule: \(\frac{d}{dx}[x^n] = nx^{n-1}\).

Thus, \(\frac{d}{dx}[6x^{-2}] = 6(-2)x^{-3} = -12x^{-3}\).

Combining these, the derivative is \(4 - 12x^{-3}\).