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$y=2(\sin^4 x+\cos^4 x+\sin^2 x\cos^2 x)^2-(\sin^8 x+\cos^8 x)$
$y=2(\sin^4 x+\cos^4 x)^2+4\sin^2 x\cos^2 x(\sin^4 x+\cos^4 x)+2\sin^4 x\cos^4 x-(\sin^4 x+\cos^4 x)^2+2\sin^4 x\cos^4 x$
$y=(\sin^4 x+\cos^4 x)^2+4\sin^2 x\cos^2 x(\sin^4 x+\cos^4 x)+4\sin^4 x\cos^4 x$
$y=(\sin^4 x+\cos^4 x+2\sin^2 x\cos^2 x)^2$
$y=(\sin^2 x+\cos^2 x)^4$
$y=1$
$\Rightarrow y'=0.$
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