Given f(x,y)=x22x2y3+6y6\displaystyle {f{{\left({x},{y}\right)}}}=-{x}^{{2}}-{2}{x}^{{2}}{y}^{{3}}+{6}{y}^{{6}}, find

fx(x,y)\displaystyle {{f}_{{{x}}}{\left({x},{y}\right)}} =  

fy(x,y)\displaystyle {{f}_{{{y}}}{\left({x},{y}\right)}} =  

fxx(x,y)\displaystyle {{f}_{{{x}{x}}}{\left({x},{y}\right)}} =  

fxy(x,y)\displaystyle {{f}_{{{x}{y}}}{\left({x},{y}\right)}} =