請問:f(x)=x(x^2-1)^(1/2),則f"(x)=? 謝謝~?

2016-11-25 3:46 pm

回答 (1)

2016-11-25 10:46 pm
✔ 最佳答案
Sol
y=x(x^2-1)^(1/2)
y^2=x^2(x^2-1)=x^4-x^2
2yy’=4x^3-2x
y'=(2x^3-x)/[x(x^2-1)^(1/2)]=(2x^2-1)/(x^2-1)^(1/2)
y’(x^2-1)^(1/2)=2x^2-1
y’(2x)+(x^2-1)y”=4x
2x(2x^2-1)/(x^2-1)^(1/2)+(x^2-1)y”=4x
(x^2-1)y”=4x-(4x^3-2x)/(x^2-1)^(1/2)
y"=4x/(x^2-1)^(1/2)-(4x^3-2x)/(x^2-1)^(3/2)


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