Problem $1.$

Let $a$ be a real number, and

$f(x,y)=x(x^2+y^2{)}^{-\frac{3}{2}}{e}^{sin(x^{a}y)}.$

Find the value$($s$)$ of a that make$($s$)\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}(1,0)=-2($i$.$e$.$ there can be more than one$).$