Question

Use the table below to evaluate d/dx [f[g(2x)]] at x = 1

x 1 2 3 4
f(x) 6 1 8 2
f '(x) 6 1 8 2
g(x) 1 4 4 3
g '(x) 9 5 5 -4

Answer 1

first we need to differentiate using chain rule

Answer 2

(2x)'=?

Answer 3

2

Answer 4

and of course derivative of g is g'
and derivative of f is f'

so you have 2*g'(2x)*f'(g(2x))

Answer 5

now input 1 for x

Answer 6

so ive got 2*9*f'(4)?

Answer 7

so would that be 2*9*2?

Answer 8

hmm...
I understand how you got everything except that 9
that number should be something else

Answer 9

i mean 5 instead of 9

Answer 10

g'(2)
look at x=2 on the table
and then find g'(x)

Answer 11

oh yes 5 is right

Answer 12

sorry ignored your correction

Answer 13

Its okay. so would that mean 2*5*2=20. Is 20 my answer?

Answer 14

looks great to me

Answer 15

Thank you!

Answer 16

np