Explain why or why not. Determine whether the following statements are true and give an explanation or a 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, x^2 + y^2 = r^2, we have dy/dx= -x/y, for y0 and any real number r> 0.

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

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