calc. help

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I'm still having trouble with the following 2 questions: I had one reply, but I'm not sure on it still. On question 2 the answers are supposed to be equivalent and for the product and quotient I got (2(x^3+1)/x^2) but for the power rule I keep getting (2(x+1)/x^2) and then for question 1 I am soooo confused! Can someone please explain this step by step for me! Thanks!


1.
Given (x^3)(y)= -y^2 (x), find both dy/dx (treating y as a function of x) and dx/dy ( treating x as a function of y). How are dy/dx and dx/dy related?



2.
Find d/dx ((x^3-2)/x) by using the quotient rule, by using the product rule, and by power rule. Show that your answers are equivalent.
 
Question 2:

pow rule: ((x^3-2)/x) = x^2 - 2/x
y' = 2x + 2/x^2

quotient:
y' = (x(3x^2) - (x^3-2)))/x^2 = (2x^3 - 2)/x^2 = 2x + 2/x^2

product:
y' = ((x^3-2)(-1/x^2) + (1/x)(3x^2) = (-x + 2/x^2) + 3x = 2x + 2/x^2
 
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