Seja f colon straight real numbers squared rightwards arrow straight real numbers dada por f left parenthesis x comma y right parenthesis equals c ...

Seja f colon straight real numbers squared rightwards arrow straight real numbers dada por f left parenthesis x comma y right parenthesis equals c o s left parenthesis fraction numerator x y minus 1 over denominator x y plus 1 end fraction right parenthesis, as derivadas pariciais, fraction numerator partial differential f over denominator partial differential x end fraction left parenthesis x comma y right parenthesis e fraction numerator partial differential f over denominator partial differential y end fraction left parenthesis x comma y right parenthesis são, respectivamente: negative s e n left parenthesis fraction numerator x y minus 1 over denominator x y plus 1 end fraction right parenthesis fraction numerator 2 y over denominator x y plus 1 end fraction e negative s e n left parenthesis fraction numerator x y minus 1 over denominator x y plus 1 end fraction right parenthesis fraction numerator 2 x over denominator x y plus 1 end fraction. negative s e n left parenthesis fraction numerator x y minus 1 over denominator x y plus 1 end fraction right parenthesis fraction numerator 2 y over denominator left parenthesis x y plus 1 right parenthesis squared end fraction e negative s e n left parenthesis fraction numerator x y minus 1 over denominator x y plus 1 end fraction right parenthesis fraction numerator 2 x over denominator left parenthesis x y plus 1 right parenthesis squared end fraction. as derivadas parciais não estão bem definidas. c o s left parenthesis fraction numerator x y minus 1 over denominator x y plus 1 end fraction right parenthesis fraction numerator 2 y over denominator left parenthesis x y plus 1 right parenthesis squared end fraction e c o s left parenthesis fraction numerator x y minus 1 over denominator x y plus 1 end fraction right parenthesis fraction numerator 2 x over denominator left parenthesis x y plus 1 right parenthesis squared end fraction. negative s e n left parenthesis fraction numerator x y minus 1 over denominator x y plus 1 end fraction right parenthesis e negative s e n left parenthesis fraction numerator x y minus 1 over denominator x y plus 1 end fraction right parenthesis.