Compute delta(y) and dy for the given values of x and dx=delta(x)

Question

y=x^2 , x=8 , delta(x)=0.5

Delta(y)= ???

dy = ???

I got dy=8 by doing:

dy= (f prime of x)dx

dy=2xdx

dy=2xdelta(x)

dy=2*8*0.5

dy=8

but I have not clue how to find delta(y) please help!

deltay = y(x+deltax)- y(x)
= (8.5)^2 - (8)^2
= (8 + 1/2)^2 - 8^2
= 8^2 + 8 + 1/4 - 8^2= 8.25
check my work.

thanks!