Find the first and second derivatives. \[ y=\frac{2 x^{5}+6}{x^{3}} \]

Step 1 ：We are given the function \(y = \frac{2x^5 + 6}{x^3}\).

Step 2 ：We need to find the first and second derivatives of this function.

Step 3 ：First, we find the first derivative using the quotient rule. The quotient rule states that the derivative of a quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the square of the denominator.

Step 4 ：Applying the quotient rule, we get the first derivative as \(y' = 10x - \frac{3(2x^5 + 6)}{x^4}\).

Step 5 ：Next, we find the second derivative by taking the derivative of the first derivative.

Step 6 ：Applying the derivative rules, we get the second derivative as \(y'' = -20 + \frac{12(2x^5 + 6)}{x^5}\).

Step 7 ：Final Answer: The first derivative is \(\boxed{10x - \frac{3(2x^5 + 6)}{x^4}}\) and the second derivative is \(\boxed{-20 + \frac{12(2x^5 + 6)}{x^5}}\).