Differentiate the function.
\[
y=\frac{3 x^{2}-5}{2 x^{3}+3}
\]

Step 1 ：We are given the function \(y=\frac{3 x^{2}-5}{2 x^{3}+3}\) and we are asked to find its derivative.

Step 2 ：To find the derivative of a function that is a quotient of two functions, we can use 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 divided by the square of the denominator.

Step 3 ：First, we find the derivative of the numerator and the derivative of the denominator. The derivative of the numerator \(3x^{2}-5\) is \(6x\). The derivative of the denominator \(2x^{3}+3\) is \(6x^{2}\).

Step 4 ：Substitute these into the quotient rule formula, we get \(\frac{-6 x^{2}\left(3 x^{2}-5\right)+6 x\left(2 x^{3}+3\right)}{\left(2 x^{3}+3\right)^{2}}\).

Step 5 ：\(\boxed{\frac{-6 x^{2}\left(3 x^{2}-5\right)+6 x\left(2 x^{3}+3\right)}{\left(2 x^{3}+3\right)^{2}}}\) is the derivative of the function.