f(x)=(4−2x2)3 . find f''

Answer 1

Use the ^ to show exponents

f(x) = (4 - 2x^2)^3
f ' (x) = 3(4 - 2x^2)^2 (-4x) , using the chain rule
= -12x(4-2x^2)^2

f '' (x) = (-12x)(2)(4-2x^2)(-4x) + (-12)(4-2x^2)^2
= 96x^2(4-2x^2) - 12(4-2x^2)^2
= 12(4-2x^2) [ 8x^2 - (4-2x^2) ]
= 12(4-2x^2)(10x^2 - 4)
= 12(2)(2 - x^2)(2)(5x^2 - 2)
= 48(2 - x^2)(5x^2 - 2) or -48(x^2 - 2)(5x^2 - 2)

I always considered the factored form over the expanded form, but if you insist, then expand the two binomials
= 48(2 - x^2)(5x^2 - 2)
or 48(10x^2