Need help

[spice shuttle]

Find du/dv if u = y^3, y=(x/x+8), and x = v^2

I don't know how the y^3 effects the problem

[spice shuttle]

<@&727457725017096242>

[solar imp]

find du/dx and dv/dx by chain rule

[spice shuttle]

Oh I see so f(x)= x^3?

[solar imp]

no

[astral marsh]

fäf

[solar imp]

you can get the last form easily without need of writing u in terms of v or x

[spice shuttle]

got it ima give it another go

[solar imp]

wait can you see my mistake

[spice shuttle]

mistake?

[solar imp]

in this

[spice shuttle]

no

[solar imp]

there is a mistake find it if you know the chain rule

[spice shuttle]

oh I only know it using '

is it the same thing?

[solar imp]

yes

don't worry if you are wrong I'll correct you

[spice shuttle]

oh ok thank you

[solar imp]

there's only one mistake here. you just have to find it

[spice shuttle]

I'm sorry I don't know it very well in the form of d/dx

[solar imp]

just think it as normal algebra $\frac{x}{y} = \frac{x}{z}\times \frac{z}{y}$

[astral marsh]

fäf

[spice shuttle]

derivation of x respect to y?

[solar imp]

right

you can tell me then what is the correct way

[spice shuttle]

I'm not sure I just knew that was run over rise

instead of rise over run

[solar imp]

i see

now you can find each derivative

and get du/dv

[spice shuttle]

wait dy/dx was the right answer?

[solar imp]

yes

[spice shuttle]

oh ok tysm I will let you know if I got it

[solar imp]

in that way dy can cancel each other

[solar imp]

ok

[spice shuttle]

3(x/(x+8))^(2)(8/(x^(2)+8)^2)?

Is this right?

[solar imp]

you didn't find dx/dv?

[spice shuttle]

Yeah my teacher just wants us to apply the rules

but not simplify

unless he asked for it

[solar imp]

but i think you missed dx/dv

[spice shuttle]

hmmm

[astral marsh]

fäf

[spice shuttle]

oh I see I did not put in v at all

Would it work if you just multiply the whole equation by 1/(2v)

[solar imp]

yes

[spice shuttle]

oh so I can just multiply that to what I already have and I got it?

[solar imp]

yes

[spice shuttle]

so the final answer would be 3(x/(x+8))^(2)(8/(x^(2)+8)^2) x (1/2v)?

[solar imp]

,w differentiate x/(x+8)

[solar imp]

your middle term needs change

[spice shuttle]

(x+8)^(2)?

[solar imp]

yes

[solar imp]

this is right

[spice shuttle]

I see so if I replace it I got it right?

[solar imp]

yeah

pls ping me when you reply

[spice shuttle]

I see tysm for all the help!

[solar imp]

or i won't see your message until i open discord

[solar imp]

you're welcome

[spice shuttle]

I finally understand it much better

when you are done do you close the chat?

[solar imp]

idk