partial derivative

I know that the partial derivative partial_f/partial_x = lim as h->0
f(x+h,y,z,...)/h. My question is, what do you do if one of the other
variables, say y, is itself a function of x? From that definition it would
seem you do not allow y to change as you change x. Is this correct?

As a concrete example, what is partial_f/partial_x of the following:
f(x,y,z) = x + 2y + 3z
y = 4x


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