Answer
$y''$ = $16$$(2x+1)^{2}$$(5x+1)$
Work Step by Step
$y$ = $x(2x+1)^{4}$
$y'$ = $\frac{d}{dx}$$[x(2x+1)^{4}]$
$y'$ = $(x)$$\frac{d}{dx}$$(2x+1)^{4}$+$(2x+1)^{4}$$\frac{d}{dx}$$(x)$
$y'$ = $(x)$$(4)(2x+1)^{3}$$\frac{d}{dx}$$(2x+1)$+$(2x+1)^{4}$$(1)$
$y'$ = $(4x)$$(2x+1)^{3}$$(2)$+$(2x+1)^{4}$
$y'$ = $(8x)$$(2x+1)^{3}$+$(2x+1)^{4}$
$y'$ = $(2x+1)^{3}$($8x+2x+1$)
$y'$ = $(2x+1)^{3}$($10x+1$)
$y''$ = $\frac{d}{dx}$[$(2x+1)^{3}$($10x+1$)]
$y''$ = $(2x+1)^{3}$$\frac{d}{dx}$($10x+1$)+($10x+1$)$\frac{d}{dx}$$(2x+1)^{3}$
$y''$ = $(2x+1)^{3}$($10$)+($10x+1$)$(3)(2x+1)^{2}$$\frac{d}{dx}$$(2x+1)$
$y''$ = $(2x+1)^{3}$($10$)+($10x+1$)$(3)(2x+1)^{2}$$(2)$
$y''$ = $(2x+1)^{2}$$(20x+10+60x+6)$
$y''$ = $(2x+1)^{2}$$(80x+16)$
$y''$ = $16$$(2x+1)^{2}$$(5x+1)$
