Differentiating With respect To x

[Bashyboy]

So, when you differentiate a function, specifically an explicit function, where y is a function of x, you are differentiating each term with respect with x. Well, when you differentiate x with respect with x, does that mean you are trying to find out how x changes with x? What does that mean anyways? And when you differentiate y with respect to x, does that mean you are trying to figure out how y is changing with each value of x?

 

[mathman]

I am confused as to what you are looking for. However dx/dx = 1.

 

[HallsofIvy]

Yes, when you find "the derivative of y with respect to x" you are comparing the (instantaneous) rate of change of y compared to the instantaneous rate of change of x or "how fast y changes as x changes". The "derivative of x with respect to x", then, compares how fast x changes to how fast x changes and, because obviously, they change at the same rate, that derivative is, as mathman says, 1.

 

[Bashyboy]

Oh, brilliant. Thank you both. That has confirmed my thoughts.