Inverse Deltas of an Array

Jelly, 7 3 bytes

ḤḢ_

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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]

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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}.