Question

PLEASE HELP! *MEDAL* Question in pic file below

Answer 1

@xapproachesinfinity

Answer 2

@Ashleyisakitty @Loser66
@Nnesha @zepdrix

Answer 3

This is repeated chain rule:
\[
h(x) = g(f(3x)) \implies h'(x) = g'(f(3x)) \cdot f'(3x) \cdot 3 = 3g'(f(3x))f'(3x)
\]
Plug in 1 and use the table to solve.

Answer 4

can you please show me the steps

Answer 5

@myininaya

Answer 6

@dan815 can you please help? :)

Answer 7

To plug in 1 and solve, or to do the derivation?

Answer 8

@jim_thompson5910 @robtobey

Answer 9

@adotm both please :)

Answer 10

@xapproachesinfinity

Answer 11

If h(x) = g(x), then h ' (x) = g ' (x)

agreed?

Answer 12

yes :)

Answer 13

now let's say h(x) = g[ f(x) ]

we will use the chain rule to get

h ' (x) = g' [ f(x) ] * f ' (x)

right?

Answer 14

yes :)

Answer 15

so we can keep this going to go as deep as we need to

h(x) = g[ f(3x) ]

h ' (x) = g' [ f(3x) ] * f ' (3x) * 3

h ' (x) = 3*g' [ f(3x) ] * f ' (3x)

as adotm pointed out above

Answer 16

from there, you plug in x = 1 and evaluate (like you see on the attached image)

Answer 17

perfect! thank u so much :)

Answer 18

can you please help me with a couple more?

Answer 19

I'll help with one more