Product Rule and Factorisation

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

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

$\displaystyle (1-x)^{\frac{1}{2}}$

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?