Re: [微積] 商用微積分 求解
: 求答案
: 小弟沒有什麼東西可以給
: 只有一點P幣
: 一題100P
: 十題1500P
: 題目對各位高手來說應該很簡單
: 感謝 QQ
1.
(x^n)' = nx^(n-1)
f(x) = x^7 (3x^3 + 2x + 1)
= 3x^10 + 2x^8 + x^7
f'(x) = 30x^9 + 16x^7 + 7x^6
2.
f(x) = 1 - 1/(x^2 + 1)
f'(x) = -(-1)/[(x^2 + 1)^2] * 2x
= 2x/[(x^2 + 1)^2]
3.
f(x) = (x^4 + 1)/(1 - x^3)
f'(x) = [4x^3 (1 - x^3) - (x^4 + 1)(-3x^2)]/ (1 - x^3)^2
= [-4x^6 + 4x^3 + 3x^6 + 3x^2]/ (1 - x^3)^2
= [-x^6 + 4x^3 + 3x^2] / (1 - x^3)^2
4.
f(x) = x^3 (x^3 - 1)^5
f'(x) = 3x^2 (x^3 - 1)^5 + 5x^3 (x^3 - 1)^4 * 3x^2
= [3x^5 - 3x^2 + 15x^5](x^3 - 1)^4
= [18x^5 - 3x^2](x^3 - 1)^4
5.
g(t) = √[t^4 + 2t^2 + 2]
g'(t) = (1/2){1/√[t^4 + 2t^2 + 2]} * (4t^3 + 4t)
= 2t(t^2 + 1)/√[t^4 + 2t^2 + 2]
6.
y(x) = (x^2 + 2x + 1)^(-5/2)
y'(x) = (-5/2)(x^2 + 2x + 1)^(-7/2) * (2x + 2)
= -5(x + 1) (x^2 + 2x + 1)^(-7/2)
7.
g(x) = 3x^3 + 2x^2 + 3x + 5
g'(x) = 9x^2 + 4x + 3
g"(x) = 18x + 4
g"'(x) = 18
8.
(√x)^(5微分) = ((1/2)x^(-1/2))^(4微分) = ...
= (1/2)(-1/2)(-3/2)(-5/2)(-7/2)x^(-9/2)
9. 10.只給函數 沒有題目
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11/12 00:49, , 1F
11/12 00:49, 1F
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