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How do I find the answer?

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Answer 1 · 2018-01-17T04:33:34

$16 (12 x^{2} - 1)$ $16(12x^2-1)$

Explanation:

Differentiate twice! Using chain rule:

$y = {(4 x^{2} - 1)}^{2}$ $y = (4x^2 - 1)^2$
$\frac{d y}{d x} = 2 \cdot (4 x^{2} - 1) \cdot (8 x) = 64 x^{3} - 16 x$ $(dy)/(dx) = 2 * (4x^2 - 1) * (8x) = 64x^3 - 16x$

Using power rule,
$\frac{d^{2} y}{{d x}^{2}} = \frac{d}{d x} \frac{d y}{d x} = 192 x^{2} - 16 = 16 (12 x^{2} - 1)$ $(d^2y)/(dx^2) = d/(dx) (dy)/(dx) = 192 x^2 - 16 = 16(12x^2-1)$

Answer 2 · 2018-01-17T04:34:51

Answer 'D' or $\frac{d^{2} y}{{d x}^{2}} = 16 (12 x^{2} - 1)$ $(d^2y)/(dx^2)=16(12x^2-1)$

Explanation:

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)

$y = {(4 x^{2} - 1)}^{2} = 16 x^{4} - 8 x^{2} + 1$ $y=(4x^2-1)^2=16x^4-8x^2+1$

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

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

Factorising by 16 yields;

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

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