Calculating Surface Area Using Double Integrals

[Cyrus]

I see what your saying about the case for t. But what if Y is not a function of time t, but is a function of the x value. Now if we take the derivative of Y w.r.t x we get a function, y'(x).

 

[Galileo]

Then, unless x represents time (which is a rather unusual notation), you cannot interpret y'(x) as a rate of change in time.