Pblms 1,2, and 4 involve implicit differentiation-- the basic rules are:

1. When diff a fn of x do it normally

2. When diff a fn of y diff wrt to y and multiply by y '

I'll do 1) and leave the other 2 for you

y^2 + xy = 8

2y y ' + y + xy' = 0

y ' (2y +x) = -y

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

3,5, and 8 are fairly simple derivatives you should be able to do them

6 and 7 involve the equation of a tangent line

the formula for a tangent line at (a,f(a)) is

y= f ' (a) (x-a) + f(a)