Find the Rate of Change of X with Respect to P

Multiple Choice

Find the rate of change of x with respect to p. $$p = \sqrt { \frac { 200 - x } { 2 x } } , \quad 0 < x \leq 200$$

A) $- \frac { 4 x p } { 2 p ^ { 2 } + 1 }$
B) $\frac { 4 x p } { 2 p ^ { 2 } + 1 }$
C) $- \frac { 4 x } { 2 p ^ { 2 } + 1 }$
D) $\frac { 4 x } { 2 p ^ { 2 } + 1 }$
E) $- \frac { 4 x p } { 2 p + 1 }$