Let $z = \sqrt { 1 + 2 x + x y }$

Multiple Choice

Let $z = \sqrt { 1 + 2 x + x y }$ , and let $x$ and $y$ be functions of $t$ with $x ( 1 ) = 2 , y ( 1 ) = 2 , x ^ { \prime } ( 1 ) = 3$ , and $y ^ { \prime } ( 1 ) = - 6$ . Find $d z / d t$ when $t = 1$ .

A) 0
B) $- 2$
C) 4
D) $- 4$
E) 2
F) 1
G) $- 1$
H) $\frac { 2 } { 3 }$