Find $\frac { d y } { d x }$ For the Equation

Multiple Choice

Find $\frac { d y } { d x }$ for the equation $\sqrt { x y } = x - 20 y$ by implicit differentiation and evaluate the derivative at the point $( 100,4 )$ .

A) $- \frac { 1 } { 25 }$
B) $\frac { 1 } { 25 }$
C) $\frac { 3 } { 25 }$
D) $- \frac { 3 } { 25 }$
E) 0