Find the derivative of the given function. \( f(x)=\left(2 x^{4}-6 x^{2}\right)^{3} \) \( f^{\prime}(x)=[?]\left(2 x^{4}-6 x^{2}\right) \square(\square x+\square x) \)

To find the derivative of \( f(x)=(2 x^{4}-6 x^{2})^{3} \), we can employ the chain rule. First, set \( u = 2x^4 - 6x^2 \), so \( f(x) = u^3 \). By the chain rule: \[ f'(x) = 3u^2 \cdot u' \] Now, we differentiate \( u \): \[ u' = \frac{d}{dx}(2x^4 - 6x^2) = 8x^3 - 12x \] Substituting back into our derivative gives: \[ f'(x) = 3(2x^4 - 6x^2)^2(8x^3 - 12x) \] To match the given format, we have: \[ f^{\prime}(x) = [3]\left(2 x^{4}-6 x^{2}\right) [8]\left(x^3- \frac{3}{2}x\right) \] Now to uncover the blanks, we can fill in: \[ f^{\prime}(x) = 3\left(2 x^{4}-6 x^{2}\right)(8x^{3}-12x) \]