Thread: Find derivative

Hi, I need to find the derivative and I do not know what I did wrong...

y=4x/ sqt(x+1)

--> y=4x * (x+1)^-1/2 then I used the

Product Rule f(x)*g'(x) + g(x)*f'(x)

f(x)=4x
g(x)=(x=1)^-1/2


y'= 4x * -1/2 * (x+1)^-3/2 + [(x+1)^-1/2] * 4

= -2x / (x+1)^3/2 + 4 / (x+1)^1/2

= -2x / (x+1)^3/2 + 4 * (x+1) / [(x+1)^1/2] * (x+1)

= -2x + 4(x+1) / (x+1)^3/2

= -2x + 4x + 4 / (x+1)^3/2

= 2x +4 / (x+1)^3/2

= 2(x+2) / (x+1)^3/2

The solution shoud be y'= -x-4/ (x+1) ^5/2

Can anyone let me knwo what I did wrong?
Thanks!

Oh, I am sorry. I guess I just figured it out. In the solution they went on to find the second derivative - y''

So
y' = 2(x+2) / (x+1)^3/2
and
y'' = y'= -x-4/ (x+1) ^5/2