求y=(4x∧2-1)÷(x∧2-1)的n阶导数

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求y=(4x∧2-1)÷(x∧2-1)的n阶导数
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求y=(4x∧2-1)÷(x∧2-1)的n阶导数
求y=(4x∧2-1)÷(x∧2-1)的n阶导数

求y=(4x∧2-1)÷(x∧2-1)的n阶导数
y=(4x²-1)÷(x²-1)=4+[3/(x²-1)]=4+(3/2)*[1/(x-1)]-(3/2)*[1/(x+1)];
y'=-(3/2)/(x-1)²+(3/2)/(x+1)²;
y"=(3/2)(1*2)/(x-1)³-(3/2)(1*2)/(x+1)³;
……
y'(n)=(-1)^n(3/2)*n!/(x-1)^(n+1)-(-1)^n(3/2)*n!/(x+1)^(n+1)
=(3/2)*{n!/[(-x-1)^(n+1)]-n!/[(1-x)^(n+1)]};

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