Transforming the derivative of $f(x)$ using a table of values

Question

I have a table that looks like:

$$\begin{array}{c|c|c|c|c|c} x & -2 & -1 & 0 & 1 & 2\\ \hline f'(x) & 0 & -0.5 & -1 & 0.5 & 1 \end{array}. $$

And three functions to use to calculate the values of their derivatives based on f '(x):

$a(x) = f(-2x)$

$b(x) = f(x+2)$

$c(x) = f(x^2)$

Apparently the answer is to use the Chain Rule but I don't see how I can without the original function for $f(x)$? A nudge or link in the right direction is much appreciated

Answer 1

$y = f(u)\\ y' = f'(u) u'$ This is the chain rule.

$a(x) = f(-2x)\\ a'(x) = f'(-2x)(-2)\\ a'(-1) = f'(2)(-2) = -2$