having trouble simplifying

[marco213]

Hello everyone,

I have come with a problem of simplification while doing the derivative of x * (x+1)^0.5

I made the derivative, which led me to (x+1)^0.5 + 1/2(x+1)^0.5 , and I know there is a way to simplify it, and I feel stupid to not know the answer..

So far what I have tried is to put everything on the same denominator, which gives me
2(x+1) + 1 / 2(x+1)^0.5 ,
which lead to
2x+3 / 2(x+1)^0.5 ,
but the answer on the back of the exercises gives
3x+2 / 2(x+1)^0.5

What am I doing wrong? It might be my lack of

 

[Ishuda]

Hello everyone,

I have come with a problem of simplification while doing the derivative of x * (x+1)^0.5

I made the derivative, which led me to (x+1)^0.5 + 1/2(x+1)^0.5 , and I know there is a way to simplify it, and I feel stupid to not know the answer..

So far what I have tried is to put everything on the same denominator, which gives me
2(x+1) + 1 / 2(x+1)^0.5 ,
which lead to
2x+3 / 2(x+1)^0.5 ,
but the answer on the back of the exercises gives
3x+2 / 2(x+1)^0.5

What am I doing wrong? It might be my lack of

Lets back up a bit. The derivative of x (x+1)^1/2 is not (x+1)^0.5 + 1/[2(x+1)^0.5] but you are close. It is
(x+1)^0.5 + x/[2(x+1)^0.5]
which, multiplying the first term by 2(x+1)^0.5 (as you did with the incorrect answer), we get
[2(x+1) + x]/[2(x+1)^0.5] = [3x + 2] / [2 (x+1)^0.5]
as given by the back of the exercises.

 

[marco213]

Oh my god! I just forgot to wrote the x on the second step, and it finally make sense! Thanks alot