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If ` f(x) = x^2/(-9 + 6 x) `, find ` f'( x ) `. Make sure to simplify your answer.
For this problem, you need to differentiate a function that involves both polynomial and rational components. The function ` f(x) = x^2/(-9 + 6 x) ` requires the application of the quotient rule for derivatives: if `f(x)=\dfrac{j(x)}{g(x)}`, then`f^{\prime}(x)=\dfrac{j^{\prime}(x)g(x)-g^{\prime}(x)j(x)}{(g(x))^2}`.
Box 1: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Be sure your variables match those in the question
`(-18 x + 6 x^2)/(-9 + 6 x)^2`