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