
设y=³√x^2(x^2+1)/( x^2+2)^2,求y'
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y'=[³√x²/(x²+2)-³√x²/(x²+2)²]'
=2/[3׳√x(x²+2)]-2x׳√x²/(x²+2)²-2/[3³√x(x²+2)²]+³√x²(4x³+8x)/(x²+2)^4
=2(x²+2-x²-1)/[3׳√x(x²+2)²]+4׳√x²/(x²+2)³
=(2/3)(x²+2+6x)/[³√x(x²+2)³]
=2/[3׳√x(x²+2)]-2x׳√x²/(x²+2)²-2/[3³√x(x²+2)²]+³√x²(4x³+8x)/(x²+2)^4
=2(x²+2-x²-1)/[3׳√x(x²+2)²]+4׳√x²/(x²+2)³
=(2/3)(x²+2+6x)/[³√x(x²+2)³]
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