ВАРИАНТ  18

Задача 14 :: Дана функция  `and`(z = f(x, y), f(x, y) = ln(`+`(sqrt(x), sqrt(y)))) .

а) Проверить, удовлетворяет ли эта функция заданному уравнению;

б) проверить, что  

restart; -1; f := proc (x, y) options operator, arrow; ln(`+`(sqrt(x), sqrt(y))) end proc; -1; z(x, y) = f(x, y); 1

z(x, y) = ln(`+`(`*`(`^`(x, `/`(1, 2))), `*`(`^`(y, `/`(1, 2)))))

z(x, y) = ln(`+`(sqrt(x), sqrt(y)))

diff(z(x, y), x) = `+`(`/`(`*`(`/`(1, 2)), `*`(`^`(x, `/`(1, 2)), `*`(`+`(`*`(`^`(x, `/`(1, 2))), `*`(`^`(y, `/`(1, 2)))))))) 

z(x, y) = ln(`+`(sqrt(x), sqrt(y)))

diff(z(x, y), y) = `+`(`/`(`*`(`/`(1, 2)), `*`(`^`(y, `/`(1, 2)), `*`(`+`(`*`(`^`(x, `/`(1, 2))), `*`(`^`(y, `/`(1, 2)))))))) 

`+`(`*`(x, `*`(diff(f(x, y), x))), `*`(y, `*`(diff(f(x, y), y)))) =

`+`(`/`(`*`(`/`(1, 2), `*`(`^`(x, `/`(1, 2)))), `*`(`+`(`*`(`^`(x, `/`(1, 2))), `*`(`^`(y, `/`(1, 2)))))), `/`(`*`(`/`(1, 2), `*`(`^`(y, `/`(1, 2)))), `*`(`+`(`*`(`^`(x, `/`(1, 2))), `*`(`^`(y, `/`(1,... 

simplify(`+`(`*`(x, `*`(diff(f(x, y), x))), `*`(y, `*`(diff(f(x, y), y))))) = `/`(1, 2) 

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