Question

Use the table below to evaluate the d/dx[g(f(3x))] 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


My work:
D/Dx(g(f(3x)))= g'(f(3x)) * f'(3x) * 2
D/dx (g(f(3*1))))
g'(f(3*1))*f'(3*1) *2
4*3*2=24

I know 24 isn't the right answer

Answer 1

Work from inside the parentheses,
(g(f(3x))' for x=1
=(g(f(3(1)))'
=(g(f(3))'
=(g(2))' [from table]
=g'(2)
=5 [from table]