simple differention problem

[red and white kop!]

Use the substitution u= 2(x^2) + 3 to differentiate y= 1/(sqrt(2(x^2) + 3))

Alright so I’m pretty sure I got this right:
y= f(u)= 1/sqrt(u) = (u)^(-1/2)
=> dy/du = (-1/2)(u^(-3/2))= (-1/2)((2(x^2) + 3)^(-3/2))
du/dx= 4x

so dy/dx = (dy/du) x (du/dx) = -2x/(sqrt((2(x^2) + 3)^3)

However, the given answer is 2/(sqrt((2(x^2) + 3)^3)
Is this a typo?

 

[renegade05]

Appears to be, yes.

A simple check can be made:

\(\displaystyle \frac{d}{dx}(\frac{1}{\sqrt{2x^2 + 3}})=\frac{-2x}{\sqrt{(2x^2 + 3)^3}}\)