Differentiation (implicit equations) 10 points.. urgent

1) 3y² - 2y + 2xy = x³

2) x = 2y / x² - y


please show the working properly..

Question 1)

Take the derivative using implicit differentiation and the product rule:

6yy' - 2y' + [2 * 1 * y + 2 * x * y'] = 3x^2

Expand the brackets:

6yy' - 2y' + 2y + 2xy' = 3x^2

Now make y' the subject:

6yy' - 2y' + 2xy' = 3x^2 - 2y

y'(6y - 2 + 2x) = 3x^2 - 2y

y' = (3x^2 - 2y) / (6y + 2x - 2)
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Question 2)

Multiply the denominator across:

x^3 - xy = 2y

Take the derivative:

3x^2 - [1y + xy'] = 2y'

Expand the brackets and make y' the subject:

3x^2 - y - xy' = 2y'

xy' + 2y' = 3x^2 - y

y'(x + 2) = 3x^2 - y

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

3y^2 - 2y +2xy =x^3
6y dy/dx - 2dy/dx + 2x dy/dx + 2y = 3x^2
dy/dx [ 6y - 2 + 2x] = 3x^2 -2y
dy/dx = ( 3x^2 - 2y )/(6y-2+2x) answer
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x = 2y/x^2 - y
or x^3 - xy = 2y
3x^2 - x dy/dx - y = 2dy/dx
dy/dx(2 + x) = 3x^2 - y
dy/dx = ( 3x^2 - y)/( 2+x) answer