PLEASE HELP! *MEDAL* Question in pic file below

Question

anonymous · Answer

attachment

anonymous · Answer

@xapproachesinfinity

anonymous · Answer

@Ashleyisakitty @Loser66 
@Nnesha @zepdrix

anonymous · Answer

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.

anonymous · Answer

can you please show me the steps

anonymous · Answer

@myininaya

anonymous · Answer

@dan815 can you please help? :)

anonymous · Answer

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

anonymous · Answer

@jim_thompson5910 @robtobey

anonymous · Answer

@adotm both please :)

anonymous · Answer

@xapproachesinfinity

jim_thompson5910 · Answer

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

anonymous · Answer

yes :)

jim_thompson5910 · Answer

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?

anonymous · Answer

yes :)

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

anonymous · Answer

perfect! thank u so much :)

anonymous · Answer

can you please help me with a couple more?

jim_thompson5910 · Answer

I'll help with one more