Maple 14 says that your answer is correct...
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?
Your answer and working are totally correct. There are two possibilities now:
1)There's a typo in your book. ✔ .........<---This seems most probable to me.
or
2)You have solved the wrong question.
Any way you can check your answer here at this website: wolfram alpha