Question

Use the table below:
*everything attached in pic file*

Answer 1

use the chain rule and write it out first then use the table to plug in the needed values and evaluate

Answer 2

it = the derivative using the chain rule

Answer 3

you there?

Answer 4

yes :) hi, but okay can u show me the chain rule plz? :) the steps of it

Answer 5

can u write out the steps im still unsure on how to solve this.

Answer 6

\[\frac{ d }{ dx }\left[ f \left( g \left( x \right) \right) \right]=f'\left( g \left( x \right) \right)\cdot g'\left( x \right)\]

Answer 7

you have something more like ...\[\frac{ d }{ dx }\left[ f \left( g \left( h \left( x \right) \right) \right) \right]=f'\left( g \left( h \left( x \right) \right) \right)\cdot g'\left( h \left( x \right) \right)\cdot h'\left( x \right)\]

Answer 8

see if you can identify the different parts...
What is f(x)?
What is g(x)?
What is h(x)?

Answer 9

umm f(x) has multiple answers correct? 6,1,8,2
And so does g(x) : 1,4,4,3
*i dont think that's correct*
but i have no clue where the h(x) came from lol

Answer 10

what is the most inside function?

Answer 11

2x? taht's the equation that's given

Answer 12

yep and what is the derivative of that?

Answer 13

2 :)

Answer 14

ohh so we use the 2 based on the table now correct? so f(x) = 1 & g(x)=4?

Answer 15

good, and what is that function evaluated at x = 1?

Answer 16

f(x)=6 & g(x)=1

Answer 17

no, what is the value of 2x when evaluated at x = 1?

Answer 18

2:)?

Answer 19

good, so now use the table to find g'(h{x))=g'(2x)=g'(2)

Answer 20

that's equal to 5! :D

Answer 21

then why do they ask us @ x=1 if they keep making us use the 2? :)

Answer 22

yep.

so now we need f'(g(h(x)))=f'(g(2x))=f'(g(2)). what is g(2)?
then, what is f'(g(2))?

Answer 23

you have to use the most inside function... see if you follow.

Answer 24

g(2) is 4
and f'(g(2)) = 4?

Answer 25

since g(2) = 4 we need f'(g(2))=f'(4). what's f'(4)?

Answer 26

2 :)

Answer 27

so let's put it all together now...\[\frac{ d }{ dx }\left[ f \left( g \left( 2x \right) \right) \right]=f'\left( g \left( 2x \right) \right)\cdot g'\left( 2x \right)\cdot 2 =2\cdot 5 \cdot 2 = 20\]

Answer 28

ok thank u!!!!!!!!!!!!!! :) so i have to write an essay answer for this question, so would i start off with d/dx[f(g(h(x)))] = f'(g(h(x))) * g'(h(x)) * h'(x) then what would i say next? lol i feel like all the facts are kind of jumbled around

Answer 29

so would i be like: the most inside function: 2x
derivative of it: 2

Answer 30

you have to keep going in until you get to the last function... the most inside one.
I'm not a writer, I'm a math guy so i'll leave he essay to you.

Answer 31

ok :) haha thank u so much 4 ur help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! :)

Answer 32

you're welcome!