What Is the Correct Derivative of f(x) = x(√x - 1)?

[Janko2]

Homework Statement

So f(x)= x(√x-1)

Homework Equations

The Attempt at a Solution

So i understand that the derivitive of a mutiple is (f x g) prime

f'xg + fxg'

I got

(1)(√x-1) + (x)(1/2x^-1/2)

now I am stuck...

ive used the equation (f(x)-f(x))/x-a and i ended up with x^3/2 -1

but when i used (f')(g)+(f)(g)'

i get 3/2x^1/2 - 1

and now i am just really confused... i could really use some help :D

 

[gb7nash]

Is $f(x) = x(\sqrt{x}-1)$ or $f(x) = x(\sqrt{x-1})$?

I got

(1)(√x-1) + (x)(1/2x^-1/2)

Don't forget parentheses. I'm sure you mean (1)(√x-1) + (x)((1/2)x^-1/2).

 

[Janko2]

okay so f(x)= x((sqrtx) -1)

the square root only applies to x. not 1

okay so (1)(√x-1)= √x-1

(x)(√x-1)' is essentially (x)(1/2x^-1/2) is it not?

There for we have

√x-1 + (x)(1/2x^-1/2)

Now I am not sure if I am doing this right but
(x)(1/2x^-1/2)= 1/2x^1/2

Assuming i am right then we have

√x-1 + 1/2x^1/2
= (x^1/2 -1) + (1/2x^1/2)
=3/2x^1/2 - 1Now is that it?

 

[gb7nash]

That looks fine.