f(x)=x^2, and so root(y)=x. d/dx root(y)=1/2root(y), d/dx x=1. Results from the 2 previous equations:(1) * 2root(y)=dy/dx=2root(x^2)=2x.
Why is that so??
I found it on a web but dunno why, please help
Derivatives
2011-10-14 6:31 am
回答 (3)
2011-10-14 8:04 am
✔ 最佳答案
root(y)=x_____________(1)d(root (y))/dx = dx/dx
d(root (y))/dy x dy/dx = 1 <-----using chain rule
(1/2)(y^(-1/2)) x dy/dx = 1
(1/ (2root (y) )) x dy/dx = 1
so, dy/dx = 2root (y)___________(2)
Sub (1) into (2),
dy/dx = 2x
參考: ME!
2011-10-16 8:47 pm
55...but how do we get d(root (y))/dy x dy/dx = 1 from chain rules, can you explain it to me??
2011-10-14 8:08 am
y= x^2
root(y) = root(x^2)
root(y) = x
2root(y)=2x
x = root(y)
by differentiation
dx/dy = 1/(2 root(y))
y= x^2
by differentiation
dy/dx= 2x
also
2x = 2 root(x^2)
from the equation about green color, we get
2root(y)=dy/dx=2root(x^2)=2x
note that:
when
y=x^n
dy/dx= nx^(n-1)
2011-10-14 00:09:27 補充：
mistake:
from the equation about green color, we get
--->
from the equation with green color, we get
root(y) = root(x^2)
root(y) = x
2root(y)=2x
x = root(y)
by differentiation
dx/dy = 1/(2 root(y))
y= x^2
by differentiation
dy/dx= 2x
also
2x = 2 root(x^2)
from the equation about green color, we get
2root(y)=dy/dx=2root(x^2)=2x
note that:
when
y=x^n
dy/dx= nx^(n-1)
2011-10-14 00:09:27 補充：
mistake:
from the equation about green color, we get
--->
from the equation with green color, we get
參考: ME
收錄日期: 2021-04-13 18:17:45
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111013000051KK00866