Final answer:
To find the derivative of the given function, use the quotient rule. The derivative is -18x + 33 / (9x+2)^2.
Step-by-step explanation:
To find the derivative of the function y = (2x-3) / (9x+2), we can use the quotient rule. The quotient rule states that if we have a function of the form f(x) = g(x) / h(x), then the derivative is given by f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x))^2.
Applying this rule to the given function, we have y'(x) = (2 * (9x+2) - (2x-3) * 9) / ((9x+2)^2). Simplifying further, we get y'(x) = (-18x + 33) / ((9x+2)^2).