Consider the functions

g:R$2$R$,$f:R$2$R$2,$g$($x$,$y$)=$x$2$y$3$f$($u$,$v$)=($u$2+$v$2,2$u$+3$v$)$g:R$2$R$,$g$($x$,$y$)=$x$2$y$3$f:R$2$R$2,$f$($u$,$v$)=($u$2+$v$2,2$u$+3$v$)$

Then the partial derivative of the composite g$$fg$$f with respect to vv equals $...$

Question $5$Answer

a$.$

$(14$u$2+29$v$2+36$uv$)(2$v$+3)(14$u$2+29$v$2+36$uv$)(2$v$+3)$

cross out

b$.$

$($u$2+$v$2)(2$u$+3$v$)2(9$u$2+8$uv$+21$v$2)($u$2+$v$2)(2$u$+3$v$)2(9$u$2+8$uv$+21$v$2)$

cross out

c$.$

$2$v$(2$u$+3$v$)2+3($u$2+$v$2)22$v$(2$u$+3$v$)2+3($u$2+$v$2)2$

cross out

d$.$

$4($u$2+$v$2)(2$u$+3$v$)3$u$+6($u$2+$v$2)2(2$u$+3$v$)24($u$2+$v$2)(2$u$+3$v$)3$u$+6($u$2+$v$2)2(2$u$+3$v$)2$

cross out

e$.$

$$none of these.