设y=(x-1)²/x则y'
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解法一：先化简，再求导
y=(x-1)²/x
=(x²-2x+1)/x
=x-2+ 1/x
y'=(x-2 +1/x)'
=1-0 -1/x²
=1- 1/x²
解法二：直接求导
y=(x-1)²/x
y'={[(x-1)²]'·x-(x-1)²·x'}/x²
=[2(x-1)·(x-1)'·x-(x-1)²·1]/x²
=[2(x-1)x-(x-1)²]/x²
=(x-1)(2x-x+1)/x²
=(x-1)(x+1)/x²
=(x²-1)/x²
=1- 1/x²
y=(x-1)²/x
=(x²-2x+1)/x
=x-2+ 1/x
y'=(x-2 +1/x)'
=1-0 -1/x²
=1- 1/x²
解法二：直接求导
y=(x-1)²/x
y'={[(x-1)²]'·x-(x-1)²·x'}/x²
=[2(x-1)·(x-1)'·x-(x-1)²·1]/x²
=[2(x-1)x-(x-1)²]/x²
=(x-1)(2x-x+1)/x²
=(x-1)(x+1)/x²
=(x²-1)/x²
=1- 1/x²
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