## anonymous 3 years ago Determine f(x) for this derivative

1. anonymous

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

2. anonymous

bro just intigrate

3. Luigi0210

Wait are you finding the anti derivative..?

4. anonymous

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

5. DDCamp

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

6. anonymous

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

7. anonymous

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

8. anonymous

hmm, still confused

9. anonymous

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10. anonymous

11. Luigi0210

Distrubute and then combine like terms

12. anonymous

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

13. anonymous

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

14. anonymous

lol idk anymore

15. anonymous

My mind r gone.

16. anonymous

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17. anonymous

burhan

18. bahrom7893

Is there a party going on here?

19. .Sam.

Yes

20. anonymous

thanks bahrom

21. anonymous

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

22. anonymous

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

23. anonymous

burhan u understand brother

24. anonymous

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

25. .Sam.

$\large f(x)=\int\limits\limits (-12x^2+8)(2x^2-4x)+(-4x^3+8x)(4x-4) dx$ $=\int\limits\limits (4 x-4) \left(8 x-4 x^3\right) \, dx+\int\limits\limits \left(8-12 x^2\right) \left(2 x^2-4 x\right) \, dx$ 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. anonymous

Oh I see. Thank you.

27. anonymous

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

28. anonymous
29. anonymous

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30. .Sam.

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

31. anonymous

that's what i was thinking

32. anonymous

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. anonymous

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. anonymous

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

35. anonymous

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. anonymous

"... 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

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