數學 微分

ln(y) = ln(x-1) + ln(x-2) + ln(x-3) + ln(x-4) - ln(x+1) - ln(x+2) - ln(x+3) - ln(x+4)

微分

(1/y)(dy/dx) = 1/(x-1) + 1/(x-2) + 1/(x-3) + 1/(x-4) - 1/(x+1) - 1/(x+2) - 1/(x+3) - 1/(x+4)

代入 (x, y) = (0, 1),
dy/dx = -1/1 - 1/2 - 1/3 - 1/4 - 1/1 - 1/2 - 1/3 - 1/4 = -25/6

因此, 所求的直線通過 (0, 1) 並有斜率 -25/6

即
y = -25/6 x + 1

或

25x + 6y - 1 = 0

https://www.wolframalpha.com/input/?i=tangent+line+of+y%3D%28x-1%29%28x-2%29%28x-3%29%28x-4%29+%2F%28%28x%2B1%29%28x%2B2%29%28x%2B3%29%28x%2B4%29+%29+at+x%3D0

這次沒有精美的版面～

2014-12-10 00:55:55 補充：
所以解答贈點要÷2～