Determine f(x) for this derivative

- anonymous

Determine f(x) for this derivative

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- anonymous

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

- anonymous

bro just intigrate

- Luigi0210

Wait are you finding the anti derivative..?

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## More answers

- anonymous

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

- DDCamp

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

- anonymous

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

- Jhannybean

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

- anonymous

hmm, still confused

- anonymous

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- Jhannybean

oh dear lord your writing...

- Luigi0210

Distrubute and then combine like terms

- anonymous

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

- Jhannybean

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

- anonymous

lol idk anymore

- Jhannybean

My mind r gone.

- anonymous

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- anonymous

burhan

- bahrom7893

Is there a party going on here?

- .Sam.

Yes

- anonymous

thanks bahrom

- Jhannybean

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

- anonymous

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

- anonymous

burhan u understand brother

- Jhannybean

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

- .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
\[\int\limits x^ndx=\frac{x^{n+1}}{n+1}+c\]
\[f(x)=\left(-8 x^5+16 x^4+16 x^3-32 x^2\right)+c\]

- Jhannybean

Oh I see. Thank you.

- anonymous

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

- anonymous

http://www.youtube.com/watch?v=QHaVc5i-Dzs

- anonymous

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- .Sam.

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

- anonymous

that's what i was thinking

- 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.

- 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.

- anonymous

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

- 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.

- 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

- mathstudent55

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