- #1
Peter G.
- 442
- 0
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. x2+y2 = 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!
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. x2+y2 = 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!