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Hi everybody,

I'm having a little difficulty understanding the differentiation of x with respect to x. When a function, f(x) is differentiated, each term is differentiated with respect to x, correct? So, when differentiating y=x, we would have d(y)/dx = d(x)/dx. To my (very limited) knowledge, dy/dx can be stated as the observed change in y for a given change in x (please correct me if I'm wrong). Applying this same logic, dx/dx can be stated as an observed change in x for a given change in x. This is where I'm hung up; how is it possible to compare the rate of change of x to itself?

My intuition (which is obviously faulty) tells me that in order to determine a rate of change, a second variable (in this case, y) must be involved.

I'd greatly appreciate any insight as I'm missing something quite trivial.

Thanks!

I'm having a little difficulty understanding the differentiation of x with respect to x. When a function, f(x) is differentiated, each term is differentiated with respect to x, correct? So, when differentiating y=x, we would have d(y)/dx = d(x)/dx. To my (very limited) knowledge, dy/dx can be stated as the observed change in y for a given change in x (please correct me if I'm wrong). Applying this same logic, dx/dx can be stated as an observed change in x for a given change in x. This is where I'm hung up; how is it possible to compare the rate of change of x to itself?

My intuition (which is obviously faulty) tells me that in order to determine a rate of change, a second variable (in this case, y) must be involved.

I'd greatly appreciate any insight as I'm missing something quite trivial.

Thanks!

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