An example of implicit differentation in Stewart, 6th ed, p 883, is given as follows: x^3 + y^3 + z^3 + 6xyz = 1 Differentiating to find dz/dx, 3x^2 + 3z^2(dz/dx) + 6yz + 6xy(dz/dx) = 0 where the product rule was used to differentiate 6xyz with respect to x. Why isn't the product rule also used when differentiating explicitly? e.g. if z = xy, dz/dx = y. rather than dz/dx = dx/dx(y) + dy/dx(x). Thanks.