The following piece of Mathematica code calculates the total derivative of a function $f(x,y(x))$ and compares it with what it should be. However, the result is not zero:
ff = f[x,y[x]]; Dt[ff,x] - (D[ff,x] + D[ff,y[x]] y'[x]) // FullSimplify
I can see that that
gives the total derivative as well and not $\partial f/\partial x$ while keeping $y(x)$ fixed. What am I missing here?