СССР in MAPLE

ВАРИАНТ  18

Задача 15 :: Найти частные производные сложной функции

 `and`(z = f(x, y), f(x, y) = `+`(`*`(x, `*`(exp(y))), `*`(y, `*`(exp(x))))), где `and`(x = x(u, v), x(u, v) = `+`(u, v)), `and`(y = y(u, v), y(u, v) = `+`(u, `-`(v)))   

restart; -1; x := proc (u, v) options operator, arrow; `+`(u, v) end proc; -1; y := proc (u, v) options operator, arrow; `+`(u, `-`(v)) end proc; -1; f := proc (x, y) options operator, arrow; `+`(`*`(...

restart; -1; x := proc (u, v) options operator, arrow; `+`(u, v) end proc; -1; y := proc (u, v) options operator, arrow; `+`(u, `-`(v)) end proc; -1; f := proc (x, y) options operator, arrow; `+`(`*`(...

z(u, v) = `+`(`*`(`+`(u, v), `*`(exp(`+`(u, `-`(v))))), `*`(`+`(u, `-`(v)), `*`(exp(`+`(u, v)))))

diff(z(u, v), u) = `+`(exp(`+`(u, `-`(v))), `*`(`+`(u, v), `*`(exp(`+`(u, `-`(v))))), exp(`+`(u, v)), `*`(`+`(u, `-`(v)), `*`(exp(`+`(u, v))))) 

z(u, v) = `+`(`*`(`+`(u, v), `*`(exp(`+`(u, `-`(v))))), `*`(`+`(u, `-`(v)), `*`(exp(`+`(u, v)))))

diff(z(u, v), v) = `+`(exp(`+`(u, `-`(v))), `-`(`*`(`+`(u, v), `*`(exp(`+`(u, `-`(v)))))), `-`(exp(`+`(u, v))), `*`(`+`(u, `-`(v)), `*`(exp(`+`(u, v))))) 

 

diff(z(u, v), u) = `+`(`*`(exp(`+`(u, `-`(v))), `*`(`+`(u, v, 1))), `*`(`+`(u, `-`(v), 1), `*`(exp(`+`(u, v))))) 

diff(z(u, v), v) = `+`(`*`((exp(`+`(u, `-`(v))))(`+`(1, `-`(u), `-`(v))), `*`(exp(`+`(u, `-`(v))))), `*`(`+`(u, `-`(v), `-`(1)), `*`(exp(`+`(u, v))))) 

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