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Differentiation Product Rule Question

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1. Hi, just wondering whether someone would be able to point out to me where I'm going wrong.

Question 1a) xsqrt(x+1)
I did: xsqrt(x+1) = x(x+1)^1/2
u=x and differentiating this gave 1
v=(x+1)^1/2 so I split this up to differentiate it
a=(x+1) and differentiating this gave me 1
and b=a^1/2 and when differentiated this gave me 1/2 a^-1/2
meaning the overall differentiation of v with respect to x was 1/2(x+1)^-1/2
I then used the product rule to get dy/dx which was 1/2x(x+1)^-1/2 + (x+1)^1/2
but this isn't what they got as the answer, any help would be greatly appreciated,
thank you!
2. Could you tell me what the real answer?
3. (Original post by Ajsc)
Could you tell me what the real answer?
The book says the answer is (3x+2) / 2sqrt(x+1)
4. Your differentiation is right, you just need to rearrange it into that form. Try factorising out 1/2(x+1)^-1/2

5. This is how I got it, sorry for the mess but hopefully you understand lol
6. (Original post by Ajsc)

This is how I got it, sorry for the mess but hopefully you understand lol
Yeah I understand, thank you so much

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