Determine whether the following statements are true and give an explanation or counterexample.

a. For any equation containing the variables x and y, the derivative dy/dx can be found by first using algebra to rewrite the equation in the form y = f(x).

b. For the equation of a circle of radius r, x² + y² = r², we have dy/dx = -x/y, for y ≠ 0 and any real number r > 0.

c. If x = 1, then by implicit differentiation, 1 = 0.

d. If xy = 1, then y' = 1/x.