Use the table to evaluate d/dx

Question

Use the table below to evaluate  at x = 1.

x	1	2	3	4
f(x)	6	1	2	2
f '(x)	6	1	10	2
g(x)	1	4	4	3
g '(x)	4	5	7	-4

Answer 1

Using the chain rule,

For the first term (g'(f(2x)) since x = 1, then 2x = 2*1 = 2 so f(2x) = f(2) and according to the table f(2) = 1 and g'(1) = 4 so the first term equals 4

For the 2nd term (f'(2x)), since x = 1, then 2x = 2*1 = 2 so f'(2x) = f'(2) and according to the table f'(2) = 1 so the 2nd term equals 1

The 3rd term just equals 2

so (g(f(2x))' = 4*1*2 = 8