find the derivative of the following function.

[lofty wedge]

Product rule (uv)' = u'v + uv'

[queen crow]

i did that the math algebra part of it is what i am stuck on

[lofty wedge]

u=x^2 and v=(x-3)^4

tell me what u' and v' are

[queen crow]

i got x^2*4(x-3)^3+(x-3)^4(2x)

[lofty wedge]

that is correct

if you wanna be fancy you can also factor

$y' = 2(x-3)^3 (2x^2 + x(x-3))$

[cosmic vapor]

al8628

[lofty wedge]

$y'=6x(x-3)^3(x-1)$

[cosmic vapor]

al8628

[lofty wedge]

but this should not be necessary

[noble verge]

Not this again

[queen crow]

i am stuck x^2*4(x-3)^3+(x-3)^4(2x) how do i factor it out

[lofty wedge]

it's not necessary

this is the initial problem

[queen crow]

my teacher wanted to apply the algebra once you find the derivate that why i came here

[lofty wedge]

that is not written in the problem statement and I am not clairvoyant

you should formulate your question more precisely

if the above is not sufficient

[noble verge]

You did so much algebra trying to find the derivative using the definition and you find trouble on this?? Lol. Just factor out x(x-3)^3

[lofty wedge]

Don't bully, please

[noble verge]

@queen crow do you feel bullied?

@lofty wedge eh bullying works. Traumatic experiences stick with us longer

[lofty wedge]

fair play

[queen crow]

i didn't apply algebra when i was doing the derivative i just know the formula but after doing it, the algebra part is what i am stuck with

[lofty wedge]

what does applying algebra mean?

are you talking about collecting common factors?

[queen crow]

yes i grouped it as doing the alegbra

[lofty wedge]

alright, I have written 2 versions of the factoring above, do you understand why they turned out like this?

[noble verge]

@queen crow yeah i will give you that there was no factorisation there only long expansion.

[queen crow]

no

[lofty wedge]

well, this is as elementary as it gets, do tell what the problem is

[queen crow]

i will take a picture of what i am doing and what i am getting stuck on here

[queen crow]

yes

[noble verge]

@queen crow still tho the factorisation here should be obvious. If not you maybe need to do many factorisation examples so you are comfortable with it.

[queen crow]

i think i figured it out