M2 Differentiation differentiate y=(x^2+1) (x^2-4)^(-1)?
回答 (3)
2015-08-26 5:40 am
用quotient rule
(2 x)/(-4 + x^2) - (2 x (1 + x^2))/(-4 + x^2)^2
(2 x)/(-4 + x^2) - (2 x (1 + x^2))/(-4 + x^2)^2
2015-08-26 2:26 pm
y=(x^2+1) (x^2-4)^(-1)
dy/dx=(x^2+1)(-1)(2x)(x^2-4)^(-2)+(2x)(x^2-4)^(-1)
dy/dx=-2x(x^2+1)(x^2-4)^-2 +2x(x^-4)^-1
dy/dx=[2x/(x^2-4)][1-(x^2+1)/(x^2-4)]
dy/dx=(x^2+1)(-1)(2x)(x^2-4)^(-2)+(2x)(x^2-4)^(-1)
dy/dx=-2x(x^2+1)(x^2-4)^-2 +2x(x^-4)^-1
dy/dx=[2x/(x^2-4)][1-(x^2+1)/(x^2-4)]
收錄日期: 2021-04-18 00:04:55
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