Question

I need help applying chain rule !
Suppose that f(x)=4x^2(3-5x)^3
Find the equation for the line to the graph of f at x=-2
I thought of using (f'g-fg')/ g^2

Answer 1

? how is that a chain rule?

Answer 2

chain rule would be the derivative of the outer function multiplied by the derivative of the inner function

Answer 3

so we have
h(x) = (x+2)^3
h' = 3(x+2)^2 * 1

here's the technique
(x+2) = u; so u^3 = (x+2)^3 which leads us to the derivative of u^3 to be 3u^2 = 3(x+2)^2

then we still need to obtain the derivative of the inner function
(x+2)' = 1

Answer 4

Where did you get (x+2) ?

Answer 5

just my own example so I won't end up doing your homework for you. I teach concepts not give out answers

Answer 6

Sorry I noticed, I just wanted to understand.

Answer 7

Thank you for your example I'll work out the problem from here and see if I can come up with the correct answer :)

Answer 8

okay
let me know if you need further clarification.

Answer 9

I understand the example but I'm having trouble with the 4x^2

Answer 10

you mentioned I thought of using (f'g-fg')/ g^2
this is quotient rule btw

Answer 11

In my case
f(x)=4x^2(3-5x)^3
f(x)=4x^2 ----> f'(x)=8x
g(x)=(3-5x)^3 --> g'(x)=3(3-5x)^2
and I would get g'(f(x))f'(x)
so 3(8x)^2*(8(3(3-5x)^2)
I really am trying, I've been stuck on this problem for a bit now :/

Answer 12

so after you do the chain rule, 4x^2 juts indicates that you multiply it
leading to a product rule

Answer 13

Is my work right so far ?

Answer 14

your chain rule is incomplete
(3-5x) needs a derivative as well

Answer 15

the derivative of (3-5x) would be -5

Answer 16

k so make sure you put them together first

Answer 17

3(3-5x)^2 * -5

Answer 18

Oh okay

Answer 19

so I would have -15(3-5x)^2

Answer 20

go on

Answer 21

3(8x)^2 *(8(-15(3-5x)^2) ?

Answer 22

where did you get the constant 8?

Answer 23

I mean to write 8x which is the derivative of 4x^2

Answer 24

rewrite it clearer

Answer 25

so my work in the top was not right ?
I took the derivative of 4x^2 = 8x
the derivative of (3-5x)^3 = 3(3-5x)^2
and you told me to take another derivative of (3-5x) = -5
I've understood this but now I'm getting lost into how to put all this together

Answer 26

product rule: u'v + uv'
f(x)=4x^2(3-5x)^3
u = 4x^2; u' = 8x
v = (3-5x)^3; v' = 3(3-5x)^2 * -5 or -15(3-5x)^2
now just do the product rule

Answer 27

8x(3-5x)^3 + (4x^2)(-15(3-5x)^2) would be my setup ?
For this particular problem to find my slope for the tangent line equation that I'm supposed to find can I automatically plug in x=-2 right away ?

Answer 28

correct set up
you can plug x = -2 right away if you want, but simplifying would be the best way to go

Answer 29

Oh okay thank you, thank you so much for your time and help !! I understand this concept a bit better :)

Answer 30

be sure to watch this
http://youtu.be/6kScLENCXLg?t=2m36s

and this one
https://www.youtube.com/watch?v=zwuQAOFvIV4

Answer 31

Okay :) thank you .

Answer 32

they are really good examples