請微分
F(X)=(X^2+3x+9)(x^2-x+15)
什麼是函數?
2010-10-10 7:20 pm
回答 (3)
2010-10-10 7:26 pm
✔ 最佳答案
f'(x)=(X^2+3x+9)d/dx(x^2-x+15)+(x^2-x+15) d/dx(X^2+3x+9)=(X^2+3x+9)(2x-1)+(x^2-x+15)(2x+3)
=2x^3+6x^2+18x-x^2-3x-9+2x^3-2x^2+30x+3x^2-3x+45
=4x^3+6x^2+42x+36
2010-10-10 8:14 pm
d/dx (x^2-x+15) = 2x-1 (By sum rule and power rule)
2010-10-10 7:34 pm
另一方法：
f(x)
= (x² + 3x + 9)(x² - x + 15)
= x⁴ - x³ + 15x² + 3x³ - 3x² + 45x + 9x² - 9x + 135
= x⁴ + 2x³ + 21x² + 36x + 135
f'(x)
= 4x³ + 6x² + 42x + 36
f(x)
= (x² + 3x + 9)(x² - x + 15)
= x⁴ - x³ + 15x² + 3x³ - 3x² + 45x + 9x² - 9x + 135
= x⁴ + 2x³ + 21x² + 36x + 135
f'(x)
= 4x³ + 6x² + 42x + 36
收錄日期: 2021-04-13 17:34:19
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20101010000051KK00373