F4,,A-MATHS,,DY/DX,,

1.
dy/dx = 1 / (x^2 + 1)^(1/2) + (-1/2) x (2x) / (x^2 + 1)^(3/2) [by product rule]
1 / (x^2 + 1)^(1/2) - x^2 / (x^2 + 1)^(3/2)

2.
dy/dx = (sec x)^2 / x - (tan x) / x^2 [ by product rule.]

2007-03-23 13:35:39 補充：
For Q1y'' = -x / (x^2 + 1)^(3/2) - 2x / (x^2 + 1)^(3/2) + 3/2 (2x) x^2 / (x^2 + 1)^(5/2) = -x / (x^2 + 1)^(3/2) - 2x / (x^2 + 1)^(3/2) + 3x^3 / (x^2 + 1)^(5/2)

2007-03-23 13:35:52 補充：
For Q2y'' = 2sec x (sec x tan x) / x - (sec x)^2 / x^2 - (sec x)^2 / x^2 + 2 tan x / x^3 = 2 (sec x)^2 tan x / x - (sec x)^2 / x^2 - (sec x)^2 / x^2 + 2 tan x / x^3

(1)

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(2)

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