СССР in MAPLE

ВАРИАНТ  18

Задача 13 :: Найти частные производные первого порядка ,

и полный дифференциал dz  функции `and`(z = f(x, y), f(x, y) = ln(`+`(`*`(3, `*`(`^`(x, 2))), `-`(`*`(`^`(y, 2)))))) 

restart; -1; f := proc (x, y) options operator, arrow; ln(`+`(`*`(3, `*`(`^`(x, 2))), `-`(`*`(`^`(y, 2))))) end proc; -1; z(x, y) = f(x, y); 1

z(x, y) = ln(`+`(`*`(3, `*`(`^`(x, 2))), `-`(`*`(`^`(y, 2)))))

 

z(x, y) = ln(`+`(`*`(3, `*`(`^`(x, 2))), `-`(`*`(`^`(y, 2)))))

diff(z(x, y), x) = `+`(`/`(`*`(6, `*`(x)), `*`(`+`(`*`(3, `*`(`^`(x, 2))), `-`(`*`(`^`(y, 2))))))) 

 

z(x, y) = ln(`+`(`*`(3, `*`(`^`(x, 2))), `-`(`*`(`^`(y, 2)))))

diff(z(x, y), y) = `+`(`-`(`/`(`*`(2, `*`(y)), `*`(`+`(`*`(3, `*`(`^`(x, 2))), `-`(`*`(`^`(y, 2)))))))) 

dz = `+`(`*`(diff(f(x, y), x), `*`(dx)), `*`(diff(f(x, y), y), `*`(dy))) 

dz = `+`(`/`(`*`(6, `*`(x, `*`(dx))), `*`(`+`(`*`(3, `*`(`^`(x, 2))), `-`(`*`(`^`(y, 2)))))), `-`(`/`(`*`(2, `*`(y, `*`(dy))), `*`(`+`(`*`(3, `*`(`^`(x, 2))), `-`(`*`(`^`(y, 2))))))))

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