i got my test back, and i need to make corrections. parts of the questions i got only partial credit, while others i have no clue what to do.

1. Part 1. If $\displaystyle 3x^2+2xy+y^2=2$, then the value of $\displaystyle \frac{dy}{dx}$ at $\displaystyle x=1$ is: A. -2 B. 0 C. 2 D. 4

I already figured out the derivative, which is $\displaystyle y'=\frac{-y^2}{2xy-2}$. Now I just have to solve for y. How do I do so?

Part 2. Find allpointson the curve where the slope is 0.

Clueless on this part.

Part 3. Write the equation of each vertical tangent line to the graph of f. (Hint: Vertical lines are x=#)

I'm pretty sure this part is connected with part 2.

2. How fast are the sides of a square changing at the instant when its sides are 6 feet long and its area is decreasing at a rate of 2 square feet per seconds?

How would I find the rate? Do I take the derivative of the equation for area of a square? Some feedback would be nice.

3. Let f and g be differentiable functions and let the values of $\displaystyle f$,$\displaystyle g$, and the derivatives $\displaystyle f'$ and $\displaystyle g'$ at x=1 and x=2 be given by the table below:

$\displaystyle x | f(x) | g(x) | f'(x) | g'(x)$

1 | 4 | 2 | 6 | 5

2 | 3 | 1 | 7 | 8

Determine the values of each of the following:

a. The derivative of $\displaystyle f+g$ at $\displaystyle x=2$

b. The derivative of $\displaystyle fg$ at $\displaystyle x=2$

c.The derivative of $\displaystyle \frac{f}{g}$ at $\displaystyle x=2$

d.$\displaystyle h'(2)$ where $\displaystyle h(x)=f(g(x))$

I already got the answers for a-c (15, 56, 7/8 respectively), and I only need help with letter d.