Derive and simplify 8√(x^4-4x^2)

[faustudent]

Derive and simplify 8√(x^4-4x^2)

I have the answer as: f'(x)=8(1/2)(x^4-4x^2)^-1/2*(4x^3-8x)
And when i simplify, i get this: f'(x)=16x^3-32x/√(x^4-4x^2)

But when i simplify this i get the wrong answer according to the Princeton Review Book i am using. I should get f'(x)=16x^2-32/√(x^2-4)

 

[serds]

f'(x)= (4*(4x^3-8x))/(√(x^4-4x^2))
Now simplify.
Hint:
x^4-4x^2= x^2(x^2-4)
4*(4x^3-8x)=16x(x^2-2)

 

[HallsofIvy]

Actually, \(\displaystyle \sqrt{x^2}= |x|\), not "x", so, unless the problem specifies that x is not negative, that answer is incorrect.

Either \(\displaystyle f'(x)= \frac{16x^3- 32x}{\sqrt{x^4- 4x^2}}\) or \(\displaystyle f'(x)= sgn(x)\frac{16x^2- 32}{\sqrt{x^2- 4}}\)