Differentiation 1

Calculus Level 3

Suppose $A=\frac { dy }{ dx }$ of ${ x }^{ 2 }+{ y }^{ 2 }=4$ at $\left( \sqrt { 2 } ,\sqrt { 2 } \right) ,B=\frac { dy }{ dx }$ of $\sin { y } +\sin { x } =\sin { x } .\sin { y }$ at $\left( \pi ,\pi \right)$ and $C=\frac { dy }{ dx }$ of ${ 2e }^{ xy }+{ e }^{ x }{ e }^{ y }-{ e }^{ x }-{ e }^{ y }={ e }^{ xy+1 }$ at $\left( 1,1 \right)$ , then $(A+B+C)$ has a value equal to

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