The quotient rule states that if you have a function \( y = \frac{u(x)}{v(x)} \), then its derivative \( y' \) is given by:
\[
y' = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}
\]
In this case, \( u(x) = x^3 \) and \( v(x) = (3x-4)^2 \).
First, we find the
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