1. Given that f(x) = [g(x)]⁴, g(0) =3, g'(0)= -1, find f'(0).

2. Using implicit differentiation, find the equation of the tangent line to the circle x² + y² = 3y at the point (1,2).

3. Consider the function g(x) = log₃[squareroot(x) (x-1)].

a) Find g'(x) using the chain rule.

b) Simplify g'(x) using properties of logarithms and then find g'(x).

c) Show that answer from b is equivalent to answer from a).