等上岸

NSS MIA BK2 Ex9A 52

Differentiate
X=cos(y/x)

Why ans is (y／x)-cot(y/x)

睇答案既解係Sin y/x /x 突變tan y／x， 諗唔明∼

thanks for the help！

cwk7093942

引用:

原帖由 等上岸 於 2014-3-21 09:13 PM 發表
NSS MIA BK2 Ex9A 52

Differentiate
X=cos(y/x)

Why ans is (y／x)-cot(y/x)

睇答案既解係Sin y/x /x 突變tan y／x， 諗唔明∼

thanks for the help！

given that x = cos(y/x)

cwk7093942

如果你先 make y in terms of x 會更容易搵到 y'

等上岸

Ar hahaha thx~ forgot to look at the question again~

How to make y as subject? There will be arc cos and I don't know how to differentiate

桃子

引用:

原帖由 cwk7093942 於 2014-3-21 09:37 PM 發表
如果你先 make y in terms of x 會更容易搵到 y'

It's not a good idea here.
By taking inverse cos, you have actually restricted the domain.
You are only dealing with a subset of given implicit function.

A simpler example is:
x=y^2
The derivative is dy/dx=1/(2y) and y can be either +ve or -ve.

This is different from y=sqrt(x) and dy/dx=1/[2sqrt(x)], where y must be +ve. (only a subset of the original function)