# Product Rule and Factorisation

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#1
I was hoping someone might be able to help show me where I am going wrong with the following:

y=2x√(1-x) use the product rule to differentiate and then factorise fully the resulting functions.

I have uploaded a picture of my workings to try and show it simpler than typing, the answer is apparently ((1-x)⌃-1/2)[2-3x] though, and I'm unsure of whether I have gone wrong on the differentiating or the factorising.

Thanks

Last edited by CParker21; 1 month ago
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1 month ago
#2
(Original post by CParker21)
I was hoping someone might be able to help show me where I am going wrong with the following:

y=2x√(1-x) use the product rule to differentiate and then factorise fully the resulting functions.

I have uploaded a picture of my workings to try and show it simpler than typing, the answer is apparently ((1-x)⌃-1/2)[2-3x] though, and I'm unsure of whether I have gone wrong on the differentiating or the factorising.

Thanks

Hard to read sideways but I think you've missed out the (-1) factor you get from differentiating 1-x with respect to x.
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1 month ago
#3
(Original post by CParker21)
I was hoping someone might be able to help show me where I am going wrong with the following:

y=2x√(1-x) use the product rule to differentiate and then factorise fully the resulting functions.

I have uploaded a picture of my workings to try and show it simpler than typing, the answer is apparently ((1-x)⌃-1/2)[2-3x] though, and I'm unsure of whether I have gone wrong on the differentiating or the factorising.

Thanks

Think about the derivative of this again. What you wrote was wrong.
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1 month ago
#4
Do it slowly step by step, u= ,u’= , v= , v’=
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#5
(Original post by Prince Philip)

Think about the derivative of this again. What you wrote was wrong.
I'm still a bit lost there, if you're finding the derivative of (x)⌃n then dy/dx = n(x)⌃n-1? So n=1/2 and x=(1-x) in this instance?

Edit, ignore me, I completely forgot about the chain rule. Finally makes sense now, thanks for your help everyone.
Last edited by CParker21; 1 month ago
1
1 month ago
#6
(Original post by CParker21)
I'm still a bit lost there, if you're finding the derivative of (x)⌃n then dy/dx = n(x)⌃n-1? So n=1/2 and x=(1-x) in this instance?
You need to use the chain rule since you have a chain of functions : and

If you're still unsure, what's the derivative of e.g. ?
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