Answer
$y''$ = $2$$(x^{3}-1)^{3}$$(136x^{6}-47x^{3}+1)$
Work Step by Step
$y$ = $x^{2}$$(x^{3}-1)^{5}$
$y'$ = $\frac{d}{dx}$[$x^{2}$$(x^{3}-1)^{5}$]
$y'$ = $(x^{2})$$\frac{d}{dx}$$(x^{3}-1)^{5}$+$(x^{3}-1)^{5}$$\frac{d}{dx}$$(x^{2})$
$y'$ = $(x^{2})$$(5)(x^{3}-1)^{4}$$\frac{d}{dx}$$(x^{3}-1)$+$(x^{3}-1)^{5}$$(2x)$
$y'$ = $(x^{2})$$(5)(x^{3}-1)^{4}$$(3x^{2})$+$(x^{3}-1)^{5}$$(2x)$
$y'$ = $(x^{3}-1)^{4}$[$15x^{4}+2x^{4}-2x$]
$y'$ = $(x^{3}-1)^{4}$$(17x^{4}-2x)$
$y''$ = $\frac{d}{dx}$[$(x^{3}-1)^{4}$$(17x^{4}-2x)$]
$y''$ = $(x^{3}-1)^{4}$$\frac{d}{dx}$$(17x^{4}-2x)$+$(17x^{4}-2x)$$\frac{d}{dx}$$(x^{3}-1)^{4}$
$y''$ = $(x^{3}-1)^{4}$$(68x^{3}-2)$+$(17x^{4}-2x)$$(4)(x^{3}-1)^{3}$$\frac{d}{dx}$$(x^{3}-1)$
$y''$ = $(x^{3}-1)^{4}$$(68x^{3}-2)$+$(17x^{4}-2x)$$(4)(x^{3}-1)^{3}$$(3x^{2})$
$y''$ = $(x^{3}-1)^{3}$[$(x^{3}-1)(68x^{3}-2)$+$(17x^{4}-2x)$$(12x^{2})$]
$y''$ = $(x^{3}-1)^{3}$$(68x^{6}-70x^{3}+2+204x^{6}-24x^{3}$]
$y''$ = $(x^{3}-1)^{3}$$(272x^{6}-94x^{3}+2)$
$y''$ = $2$$(x^{3}-1)^{3}$$(136x^{6}-47x^{3}+1)$
