d/dx(f(4x^2))=9x^2
calculate f'(x)
show me the step please
derivative calculation
2013-10-22 6:34 am
回答 (2)
2013-10-22 7:39 am
✔ 最佳答案
d(f(4x^2))/dx = 9x^2[d(f(4x^2))/d(4x^2)][d(4x^2)/dx] = 9x^2
[d(f(4x^2))/d(4x^2)][8x] = 9x^2
[d(f(4x^2))/d(4x^2)] = (9/8)x
Let y = 4x^2
d(f(y))/dy = (9/8)[(√y)/2]
= (9√y)/16
But x or y are just symbols. therefore
f'(x) = (9√x)/16
2013-10-22 7:41 am
d/dx(f(4x^2))=9x^2
integrating both sides
f(4x^2) = 3x^3 + C where C is a constant
let y = 4x^2 => x = (y/4)^(1/2)
f(y) = 3(y/4)^(3/2) + C
f'(x) = (9/8)(x/4)^(1/2)
integrating both sides
f(4x^2) = 3x^3 + C where C is a constant
let y = 4x^2 => x = (y/4)^(1/2)
f(y) = 3(y/4)^(3/2) + C
f'(x) = (9/8)(x/4)^(1/2)
收錄日期: 2021-04-27 20:40:40
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20131021000051KK00270