## burhan101 Group Title Determine f(x) for this derivative one year ago one year ago

1. burhan101 Group Title

$\large f'(x)=(-12x^2+8)(2x^2-4x)+(-4x^3+8x)(4x-4)$

2. jishan Group Title

bro just intigrate

3. Luigi0210 Group Title

Wait are you finding the anti derivative..?

4. burhan101 Group Title

@Luigi0210 yes :S & @jishan i am not allowed to integrate

5. DDCamp Group Title

First, simplify. Then you should just be able to use the power rule for anti-derivatives.

6. galacticwavesXX Group Title

then how do you find the original function if you can't integrate

7. Jhannybean Group Title

@DDCamp can you elaborate? :D Sprinkle on us your wisdom!

8. burhan101 Group Title

hmm, still confused

9. jishan Group Title

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10. Jhannybean Group Title

11. Luigi0210 Group Title

Distrubute and then combine like terms

12. galacticwavesXX Group Title

simplify the function given then integrate to get f(x)

13. Jhannybean Group Title

But he says he's not allowed to integrate? That's what's confusing me. how to you find F(x) without integrating?

14. galacticwavesXX Group Title

lol idk anymore

15. Jhannybean Group Title

My mind r gone.

16. jishan Group Title

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17. jishan Group Title

burhan

18. bahrom7893 Group Title

Is there a party going on here?

19. .Sam. Group Title

Yes

20. jishan Group Title

thanks bahrom

21. Jhannybean Group Title

Haha. I'd be able to understand how to solve this problem if only i could make out jishan's writing =_=

22. galacticwavesXX Group Title

i think he simplified the problem but its soo unclear and he also integrated

23. jishan Group Title

burhan u understand brother

24. Jhannybean Group Title

I see his integral sign but i cant make out the numbers :(

25. .Sam. Group Title

$\large f(x)=\int\limits\limits (-12x^2+8)(2x^2-4x)+(-4x^3+8x)(4x-4) dx$ $=\int\limits\limits (4 x-4) \left(8 x-4 x^3\right) \, dx+\int\limits\limits \left(8-12 x^2\right) \left(2 x^2-4 x\right) \, dx$ Expand and integrate using power rule for each term $\int\limits x^ndx=\frac{x^{n+1}}{n+1}+c$ $f(x)=\left(-8 x^5+16 x^4+16 x^3-32 x^2\right)+c$

26. Jhannybean Group Title

Oh I see. Thank you.

27. galacticwavesXX Group Title

now @.Sam. has shed light on what was unseen but i think @burhan101 misinterpreted the question

28. love_jessika15 Group Title
29. love_jessika15 Group Title

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30. .Sam. Group Title

I don't think you can find f(x) without integrating @galacticwavesXX

31. galacticwavesXX Group Title

that's what i was thinking

32. Jemurray3 Group Title

You don't need to go through anything elaborate, just look at it. It's fairly clearly a product-rule derivative, so just take the second part of the first term times the first part of the second term. You can add in a constant for good measure.

33. Jemurray3 Group Title

If you assume f(x) = g(x) * h(x), then f'(x) = g'(x)h(x) + g(x)h'(x). You can just look at the problem and go from there.

34. burhan101 Group Title

I am not allowed to integrate whatsoever for this question !!

35. Jemurray3 Group Title

I'm not talking about any integrating. Look at what I wrote, then look at the question. You can clearly see what h is, and what g is, so you know what f is.

36. RolyPoly Group Title

"... are you finding the anti derivative..?" "yes :S" I suppose finding anti-derivative is the same as integrating. If you don't like the integral sign, then you may take the limit of a sum: $\lim_{x\rightarrow \infty}\sum_{k=1}^{n} y(x_k)\Delta x$, which is the same as integrating the function. For your reference: http://www3.ul.ie/~mlc/support/Loughborough%20website/chap15/15_1.pdf

37. mathstudent55 Group Title

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