Hello, I have a couple questions, i'm not sure what im doing wrong.

1.) find the derivative

(x+1)^2(x^2+1)^-3

so I do the product rule and the chain rule to get

(2x)(x+1)^2-3(x^2+1)^-4+(x+1)(x^2+1)^-3

is this correct so far? If yes, where do I go from here?

I already have the answer I just cant figure out how to get there.

2.) Evaluate dy/dt for the function at the point.

x+y/x-y = x^2 + Y^2 , dx/dt = 12 , x = 1, y = 0

I use the quotient rule on the left side and find the derivative or the right and get

2 dy/dt = 2 dx/dt + 2 dy/dt

the answer is 12, but I dont understand how you get there if you remove the dy/dt's. 2dy/dt - 2 dy/dt to take them to one side?? I can see that if you divide all 3 by 2 the dx/dt is 12 but there's no dy/dt's left in the problem for it to be equal to? do you see what im trying to say?

Thanks