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Use logarithmic differentiation to find the derivative of the function.

$ y = (x^2 + 2)^2 (x^4 + 4)^4 $

$\left(x^{2}+2\right)^{2}\left(x^{4}+4\right)^{4}\left(\frac{4 x}{x^{2}+2}+\frac{16 x^{3}}{x^{4}+4}\right)$

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