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求当x=2时,√(x^3+3x-5)的导数是多少?
人气:115 ℃ 时间:2019-10-08 08:32:18
解答
y = √(x^3+3x-5) = (x^3+3x-5)^(1/2)
y ' = (1/2) (x^3+3x-5)^(-1/2) *(3x^2 + 3)
= (3/2)(x^3+3x-5)^(-1/2)(x^2 + 1)
x = 2,y' = (3/2)(2^3+3*2-5)^(-1/2)(2^2 + 1)
= (3/2)(8 + 6 -5)^(-1/2) *5
= (15/2)*9^(-1/2)
= (15/2)(1/3)
= 5/2
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