Implicit Differentiation and the Chain Ruleby Peter G. Tags: chain, differentiation, implicit, rule 

#1
Jun2613, 05:22 PM

P: 437

Hi,
I was trying to understand why the chain rule is needed to differentiate expressions implicitly. I began by analyzing the equation used by most websites I visited: e.g. x^{2}+y^{2} = 10 After a lot of thinking, I got to a reasoning that satisfied me... Here it goes: From my understanding, the variable y is a function of x. This function of x is being squared. This means that we can think of f(x) as part of another function (e.g. u = g(y) = y^2). Hence, y^2 is a composite function and, thus, differentiating it would require the chain rule. However, after coming across some different type of questions I am no longer sure my train of thought is valid. For example: 6x^2+17y = 0. I have read that to differentiate 17 y with respect to x we also have to apply the chain rule. This does not fit with my original reasoning (since, to my eyes, y cannot be thought of as a composite function in this case) Can anyone please help me understand why we have to use the chain rule to differentiatie implicitly? Thank you in advance! 



#2
Jun2613, 05:33 PM

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#3
Jun2613, 06:38 PM

P: 437

Oh, perfect, that is great news! I must have misread the solution to the last problem. Thank you very much!




#4
Jun2713, 03:20 PM

P: 29

Implicit Differentiation and the Chain Rule 



#5
Jun2713, 03:38 PM

P: 29





#6
Jun2713, 03:43 PM

HW Helper
P: 772

[tex] \frac{\mathrm{d}(17)}{\mathrm{d}x} = 0. [/tex] 



#7
Jun2713, 03:56 PM

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P: 20,962




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