#1. Since d/dx tan x = sec^2 x, you have
10x sec^2(5x^2)
#2. ok
#3. ok
#4. y' = x^2-1
so, 0
#5.
y = cos(1+sin)
y' = [(-sin)(1+sin)-cos(cos)]/(1+sin)^2
= (-sin-sin^2-cos^2)/(1+sin)^2
= (-sin-1)/(1+sin)^2
= -1/(1+sin)
#6.
I. No idea what ^3(sqrt x-1) means
II. y(1) = 1 or 2, so not continuous
III. y(1) = 1 or 1/2, so not continuous
So, only possible choice is I or none.