Here's the question you clicked on:
burhan101
Determine f(x) for this derivative
\[\large f'(x)=(-12x^2+8)(2x^2-4x)+(-4x^3+8x)(4x-4)\]
Wait are you finding the anti derivative..?
@Luigi0210 yes :S & @jishan i am not allowed to integrate
First, simplify. Then you should just be able to use the power rule for anti-derivatives.
then how do you find the original function if you can't integrate
@DDCamp can you elaborate? :D Sprinkle on us your wisdom!
oh dear lord your writing...
Distrubute and then combine like terms
simplify the function given then integrate to get f(x)
But he says he's not allowed to integrate? That's what's confusing me. how to you find F(x) without integrating?
lol idk anymore
Is there a party going on here?
Haha. I'd be able to understand how to solve this problem if only i could make out jishan's writing =_=
i think he simplified the problem but its soo unclear and he also integrated
burhan u understand brother
I see his integral sign but i cant make out the numbers :(
\[\large f(x)=\int\limits\limits (-12x^2+8)(2x^2-4x)+(-4x^3+8x)(4x-4) dx\] \[=\int\limits\limits (4 x-4) \left(8 x-4 x^3\right) \, dx+\int\limits\limits \left(8-12 x^2\right) \left(2 x^2-4 x\right) \, dx\] Expand and integrate using power rule for each term \[\int\limits x^ndx=\frac{x^{n+1}}{n+1}+c\] \[f(x)=\left(-8 x^5+16 x^4+16 x^3-32 x^2\right)+c\]
Oh I see. Thank you.
now @.Sam. has shed light on what was unseen but i think @burhan101 misinterpreted the question
|dw:1368926205410:dw|
I don't think you can find f(x) without integrating @galacticwavesXX
that's what i was thinking
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.
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.
I am not allowed to integrate whatsoever for this question !!
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.
"... 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
|dw:1368942664902:dw|