Inverse Deltas of an Array
Jelly, 7 3 bytes
ḤḢ_
Try it online!
Background
The deltas of (a, b, c, d) are b - a, c - b, and d - c. Cumulatively reducing (a, b - a, c - b, d - c) by subtraction yields a - (b - a) = 2a - b, 2a - b - (c - b) = 2a - c, and 2a - c - (d - c) = 2a - d, so the correct result is (2a - a, 2a - b, 2a - c, 2a - d).
How it works
ḤḢ_ Main link. Argument: A (array)
Ḥ Unhalve; multiply all integers in A by 2.
Ḣ Head; extract first element of 2A.
_ Subtract the elements of A from the result.
Python 2, 30 bytes
lambda x:[x[0]*2-n for n in x]
Test it on Ideone.
How it works
The deltas of (a, b, c, d) are b - a, c - b, and d - c. Cumulatively reducing (a, b - a, c - b, d - c) by subtractiong yields a - (b - a) = 2a - b, 2a - b - (c - b) = 2a - c, and 2a - c - (d - c) = 2a - d, so the correct result is (2a - a, 2a - b, 2a - c, 2a - d).
Mathematica, 8 bytes
2#-{##}&
Unnamed function taking an indeterminate number of arguments. This uses an "easy" way: negates the entire list and adds twice the (original) first element.
Called for example like 2#-{##}&[1,3,4,2,8]
; returns a list like {1,-1,-2,0,-6}
.