Answer
(a)
$(fgh)'$ = $fgh'+fg'h+f'gh$
(b)
putting $f$ = $g$ = $h$ in (a)
$\frac{d}{dx}[f(x)]^{3}$ = $fff'+ff'f+f'ff$ = $3fff'$ = $3[f(x)]^{2}f'(x)$
(c)
$y$ = $3(x^{4}+3x^{3}+17x+82)^{2}(4x^{3}+9x^{2}+17)$
Work Step by Step
(a)
$(fgh)'$ = $[(fg)h]'$ = $(fg)h'+(fg)'h$ = $(fg)h'+(fg'+f'g)h$ = $fgh'+fg'h+f'gh$
(b)
putting $f$ = $g$ = $h$ in (a)
$\frac{d}{dx}[f(x)]^{3}$ = $fff'+ff'f+f'ff$ = $3fff'$ = $3[f(x)]^{2}f'(x)$
(c)
$y$ = $(x^{4}+3x^{3}+17x+82)^{3}$
$y$ = $3(x^{4}+3x^{3}+17x+82)^{2}(4x^{3}+9x^{2}+17)$
