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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
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).
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