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# Help with this differentiation watch

1. How would i find the gradient function of this graph

y=((-x^4+x^2+x+3)/2)^(1/3)

basically i can't differentiate it and would love someone to help me with it

thanks
2. differentiate using the chain rule?
3. I dont know the chain rule, im only doing C3 maths at college at the minute.
4. Isn't chain rule at the start of C3?
5. all i have done of c3 at the minute is the coursework which is what i'm needing this for. im showing that the rearrangment method of f(x)=0 to x=g(x) only works when g'(x) is -1<g'(x)<1
6. If you have (F(x))^n , you basically use the standard pattern.

Ie multiply by the index (n), then subtract 1 from the index.

Then you differentiate what is in the bracket and mutiply the two results together to give the final result.

Ie to differentiate (7x)^2, you get 2(7x) and then you differentiate the bracket to get a 7, meaning the final answer is 14(7x) or 98x.
7. y=((-x^4+x^2+x+3)/2)^(1/3) if we remember rules of indices can be written:
y=((-x^4+x^2+x+3)^-2)^(1/3)
y=((-x^4+x^2+x+3)^(-2)x(1/3)
y=((-x^4+x^2+x+3)^-2/3

now in form (f(x)^n)
chain rule dy/dx= (n)(f'(x))(f(x))^n-1)
8. (Original post by stevencarrwork)
If you have (F(x))^n , you basically use the standard pattern.

Ie multiply by the index (n), then subtract 1 from the index.

Then you differentiate what is in the bracket and mutiply the two results together to give the final result.

Ie to differentiate (7x)^2, you get 2(7x) and then you differentiate the bracket to get a 7, meaning the final answer is 14(7x) or 98x.
Okay, tried my hardest to understand/follow this but i dont quite get it.

I know i wont learn anything from this, but please could someone just give me the answer as i need to finish writing the courswork tonight and this the very last section.
thanks
9. (Original post by 1k0ed1)
How would i find the gradient function of this graph

y=((-x^4+x^2+x+3)/2)^(1/3)

basically i can't differentiate it and would love someone to help me with it

thanks

I can't get the right bracket. Help
10. (Original post by davidcy147)
y=((-x^4+x^2+x+3)/2)^(1/3) if we remember rules of indices can be written:
y=((-x^4+x^2+x+3)^-2)^(1/3)
y=((-x^4+x^2+x+3)^(-2)x(1/3)
y=((-x^4+x^2+x+3)^-2/3

now in form (f(x)^n)
chain rule dy/dx= (n-1)(f'(x))(f(x))^n)
Does this not help because if you can differentiate just use this chain rule here. PM if you need help
11. chain Rule [email protected]
12. (Original post by 1k0ed1)
How would i find the gradient function of this graph

y=((-x^4+x^2+x+3)/2)^(1/3)

basically i can't differentiate it and would love someone to help me with it

thanks
I think this might be helpful.
Attached Images

13. (Original post by maxfire)
chain Rule [email protected]
havnt learnt it yet
14. diff the bracket

bring the power to the front

subtract 1 from the power

then you have (power)(diff of bracket)(bracket)^(power - 1)

(correct me if I'm wrong)
15. Cubing it and differentiating implicitly would also be a cool way to do this!

EDIT: More generally:
16. (Original post by My Alt)
Cubing it and differentiating implicitly would also be a cool way to do this!
Seriously! ...Why would you? STEP may interest you!
17. (Original post by 1k0ed1)
havnt learnt it yet

erg.
ok
if you have something in a bracket (u) to the power of something (n)

u^n

differentiates to:

n(u')(u)^(n-1)

if you get that.

so you bring the power down, and minus 1 from it like usual, and then you time it by the derivative of the funtion as well (u')

HOPE THIS HELPED
18. (Original post by davidcy147)
Seriously! ...Why would you? STEP may interest you!
It's not really any slower, and it means you dont _need_ the chain rule What do you mean STEP may interest you?!?
19. Haha Step is all about thinking outside the box, which is something you seem to do! Kudos to you though, wish I had that creative thought pattern!
20. (Original post by My Alt)
Cubing it and differentiating implicitly would also be a cool way to do this!

EDIT: More generally:
i wish i understood this

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