Suppose That X and Y Are Related by the Equation $x ^ { 3 }$

Multiple Choice

Suppose that x and y are related by the equation $x ^ { 3 }$ + $( 2 y + 1 ) ^ { 2 }$ = $y ^ { 2 }$ . Use implicit differentiation to determine $\frac { d y } { d x }$ .

A) $\frac { d y } { d x }$ = $\frac { 3 x ^ { 2 } + 4 ( 2 y + 1 ) } { 2 y }$
B) $\frac { d y } { d x }$ = 3 $x ^ { 2 }$ + 2(y + 1)
C) $\frac { d y } { d x }$ = $\frac { - 3 x ^ { 2 } } { 2 ( 3 y + 2 ) }$
D) $\frac { d y } { d x }$ = $\frac { - 3 x ^ { 2 } } { 6 y + 1 }$