1. Suppose g(x, f) = f³(x) - x = 0

Then 0 = dg = 3f²df - dx that is

We get

2. g(x, f) = xf(x) - 1 = 0

We get

and

Since f(x) = 1 / x, we get (1 / x)' = - (1 / x²)