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Answer 1 · 2018-01-17T04:33:34

#16(12x^2-1)#

Differentiate twice! Using chain rule:

#y = (4x^2 - 1)^2#
#(dy)/(dx) = 2 * (4x^2 - 1) * (8x) = 64x^3 - 16x#

Using power rule,
#(d^2y)/(dx^2) = d/(dx) (dy)/(dx) = 192 x^2 - 16 = 16(12x^2-1) #

Answer 2 · 2018-01-17T04:34:51

Answer 'D' or #(d^2y)/(dx^2)=16(12x^2-1)#

So to find the second order derivative we must differentiate it twice.

I would recommend multiplying out the brackets before doing the differential (it will make the algebra easier in the end)

#y=(4x^2-1)^2=16x^4-8x^2+1#

#:. (dy)/(dx)=64x^3-16x#

and #(d^2y)/(dx^2)=192x^2-16#

Factorising by 16 yields;

#(d^2y)/(dx^2)=16(12x^2-1)#