Answer:
7. (4x - 3xy^2 - 2y) / (3x^2y + 2x).
Step-by-step explanation:
Implicit differentiation:
7. 3x^2 y^2 = 4x^2 - 4xy
6x * y^2 + 3x^2 * 2y y' = 8x - 4(x y' + y)
6xy^2 + 6x^2y y' = 8x - 4x y' - 4y
6x^2y y' + 4x y' = 8x - 6xy^2 - 4y
y' = (8x - 6xy^2- 4y) / (6x^2y + 4x)
y' = 2(4x - 3xy^2- 2y) / 2(3x^2y + 2x)
= (4x - 3xy^2 - 2y) / (3x^2y + 2x).
Numbers 8 and 9 are done in the same way.
We use the Chain, Product and Quotient rules where applicable.
