40. 𝑧 = ln(𝑥𝑦) funksiyaning xususiy hosilalarini toping. Найдите частные производные функции 𝑧 = ln(𝑥𝑦). Find the partial derivatives of a function 𝑧 = ln(𝑥𝑦).

′ 1 ′ 1 𝑧𝑥 = 𝑥 , 𝑧𝑦 = 𝑦

′ 2 ′ 1 𝑧𝑥 = 𝑥 , 𝑧𝑦 = 𝑦

′ 1 ′ 1 𝑧𝑥 = 𝑥 , 𝑧𝑦 = − 𝑦

′ 1 ′ 1 𝑧𝑥 = − 𝑥 , 𝑧𝑦 = 𝑦

39. 𝑧 = 𝑒−3 funksiyaning xususiy hosilalarini toping. Найдите частные производные 𝜋 𝜋 функции 𝑧 = 𝑒−3 . Find the partial derivatives of a function 𝑧 = 𝑒−3 .

𝑧′ = 0, 𝑧′ = 0 𝑥 𝑦

𝑧′ = 0, 𝑧′ ≠ 0 𝑥 𝑦

𝑧′ ≠ 0, 𝑧′ = 0 𝑥 𝑦

𝑧′ = −1, 𝑧′ = 0 𝑥 𝑦

38. 𝑧 = arctg 𝑥 𝑦 𝑦 funksiyaning xususiy hosilalarini toping. Найдите частные производные функции 𝑧 = arctg 𝑥. Find the partial derivatives of a function 𝑧 = 𝑦 arctg 𝑥. 𝑦

𝑧′ = 𝑦 , 𝑧′ = − 𝑥 𝑥 𝑥2+𝑦2 𝑦 𝑥2+𝑦2

𝑧′ = 𝑦 , 𝑧′ = 𝑥 𝑥 𝑥2+𝑦2 𝑦 𝑥2+𝑦2

𝑧′ = − 𝑦 , 𝑧′ = 𝑥 𝑥 𝑥2+𝑦2 𝑦 𝑥2+𝑦2

𝑧′ = 𝑦 , 𝑧′ = − 2𝑥 𝑥 𝑥2+𝑦2 𝑦 𝜋 𝑥2+𝑦2

35. 𝑧 = 𝑥𝑦 funksiyaning uzilish nuqtalari to’plamini toping. Найдите множества точек разрыва функции 𝑧 = 𝑥𝑦. Find the sets of discontinuity points of the function 𝑧 = 𝑥𝑦.

Funksiyada uzilish mavjud emas/функция не имеет точек разрыва/function has no breakpoints

31. 𝑧 = ln √𝑥2 + 𝑦2 funksiyaning uzilish nuqtalari to’plamini toping. Найдите множествo точек разрыва функции 𝑧 = ln √𝑥2 + 𝑦2 . Find the set of discontinuity points of the function 𝑧 = ln √𝑥2 + 𝑦2.

Funksiyada uzilish nuqtalari mavjud emas/Функция не имеет точек разрыва/function has no breakpoints

30. 𝑧 = 2 𝑥2+𝑦2 funksiyaning uzilish nuqtalarini toping. Найдите точки разрыва функции 𝑧 = 2 𝑥2+𝑦2 . Find the breakpoints of the funtion 𝑧 = 2 . 𝑥2+𝑦2

funksiyaning uzilish nuqtalari mavjud emas/Функция не имеет точек разрыва/ The function has no breakpoints

26. lim𝑥→O sin(𝑥𝑦) ni hisoblang. Вычислите lim𝑥→O sin(𝑥𝑦). Calculate lim𝑥→O sin(𝑥𝑦). 𝑦→O

0 𝑥𝑦 𝑦→O 𝑥𝑦 𝑦→O 𝑥𝑦

25. lim 𝑥2𝑦 ni hisoblang. Вычислите lim 𝑥2𝑦 . Calculate lim 𝑥2𝑦 . 𝑥→O 𝑥2+𝑦2 𝑦→O

3 𝑥→O 𝑥2+𝑦2 𝑦→O 𝑥→O 𝑥2+𝑦2 𝑦→O

21. 𝑓(𝑥, 𝑦) = 𝑥𝑦 funksiya berilgan, 𝑓 (𝑥 ; 𝑦) ni hisoblang. Дана функция 𝑓(𝑥, 𝑦) = 𝑥𝑦, 𝑦 𝑥 найти 𝑓 (𝑥 ; 𝑦). Given a function 𝑓(𝑥, 𝑦) = 𝑥𝑦, calculate 𝑓 (𝑥 ; 𝑦). 𝑦 𝑥 𝑦 𝑥

𝑓 (𝑥 ; 𝑦) = 1 𝑦 𝑥

𝑓 (𝑥 ; 𝑦) = −1 𝑦 𝑥

𝑓 (𝑥 ; 𝑦) = 2 𝑦 𝑥

𝑓 (𝑥 ; 𝑦) = −2 𝑦 𝑥

22. 𝑓(𝑥, 𝑦) = 𝑥𝑦 funksiya berilgan, 𝑓(𝑥 − 𝑦; 𝑥 + 𝑦).ni hisoblang. Дана функция 𝑓(𝑥, 𝑦) = 𝑥𝑦, найти 𝑓(𝑥 − 𝑦; 𝑥 + 𝑦). Given a function 𝑓(𝑥, 𝑦) = 𝑥𝑦, calculate 𝑓(𝑥 − 𝑦; 𝑥 + 𝑦).

𝑓(𝑥 − 𝑦; 𝑥 + 𝑦) = 𝑥2 − 𝑦2

𝑓(𝑥 − 𝑦; 𝑥 + 𝑦) = 𝑥2 + 𝑦2

𝑓(𝑥 − 𝑦; 𝑥 + 𝑦) = −𝑥2 − 𝑦2

𝑓(𝑥 − 𝑦; 𝑥 + 𝑦) = −𝑥2 + 𝑦2

20. 𝑓(𝑥, 𝑦) = 𝑥𝑦 + 𝑥 𝑦 funksiya berilgan, 𝑓 (1; 𝑦) ni hisoblang. Дана функция 𝑥 𝑓(𝑥, 𝑦) = 𝑥𝑦 + 𝑥 , найти 𝑓 (1; 𝑦). Given a function 𝑓(𝑥, 𝑦) = 𝑥𝑦 + 𝑥 , calculate 𝑦 𝑥 𝑦 𝑓 (1; 𝑦). 𝑥

𝑓 (1; 𝑦) = 𝑦 + 𝑥 𝑥 𝑥 𝑦

𝑓 (1; 𝑦) = 𝑦 − 𝑥 𝑥 𝑥 𝑦

𝑓 (1; 𝑦) = − 𝑦 + 𝑥 𝑥 𝑥 𝑦

𝑓 (1; 𝑦) = − 𝑦 − 𝑥 𝑥 𝑥 𝑦

19. 𝑓(𝑥, 𝑦) = 𝑥𝑦 + 𝑥 𝑦 funksiya berilgan, 𝑓(𝑦; 𝑥) ni hisoblang. Дана функция 𝑓(𝑥, 𝑦) = 𝑥𝑦 + 𝑥 , найти 𝑓(𝑦; 𝑥). Given a function 𝑓(𝑥, 𝑦) = 𝑥𝑦 + 𝑥 , calculate 𝑓(𝑦; 𝑥). 𝑦 𝑦

𝑓(𝑦; 𝑥) = 𝑥𝑦 + 𝑦 𝑥

𝑓(𝑦; 𝑥) = 𝑥𝑦 − 𝑦 = 𝑥

𝑓(𝑦; 𝑥) = −𝑥𝑦 + 𝑦 𝑥

𝑓(𝑦; 𝑥) = −𝑥𝑦 − 𝑦

43. 𝑧 = ln(𝑥 + 𝑦) funksiyaning xususiy hosilalarini toping. Найдите частные производные функции 𝑧 = ln(𝑥 + 𝑦). Find the partial derivatives of a function 𝑧 = ln(𝑥 + 𝑦).

𝑧′ = 1 , 𝑧′ = 1 𝑥 𝑥+𝑦 𝑦 𝑥+𝑦

𝑧′ = 1 , 𝑧′ = − 1 𝑥 𝑥+𝑦 𝑦 𝑥+𝑦

𝑧′ = − 1 , 𝑧′ = 1 𝑥 𝑥+𝑦 𝑦 𝑥+𝑦

𝑧′ = 1 , 𝑧′ = 2 𝑥 𝑥+𝑦 𝑦 𝑥+𝑦

. 𝑧 = √sin 𝑥 · sin 𝑦 funksiyaning aniqlanish sohasini toping. Найдите область определения функции 𝑧 = √sin 𝑥 · sin 𝑦. Find the domain of function 𝑧 = √sin 𝑥 · sin 𝑦. 2𝜋𝑘 ≤ 𝑥 ≤ 𝜋 + 2𝜋𝑘 −𝜋 + 2𝜋𝑘 ≤ 𝑥 ≤ 2𝜋𝑘

{− 𝜋2 + 2𝜋𝑘 ≤ 𝑦 ≤𝜋 + 2𝜋𝑘2и {𝜋2+ 2𝜋𝑘 ≤ 𝑦 ≤3𝜋 2+ 2𝜋𝑘2𝜋𝑘 ≤ 𝑥 ≤ 𝜋 + 2𝜋𝑘

{𝜋 𝜋𝜋 + 2𝜋𝑘 ≤ 𝑥 ≤ 2𝜋𝑘и {𝜋 3𝜋 + 2𝜋𝑘 ≤ 𝑦 ≤ 2 + 2𝜋𝑘2 + 2𝜋𝑘 ≤ 𝑦 ≤2+ 2𝜋𝑘2 𝜋𝑘 ≤ 𝑥 ≤ 𝜋 + 𝜋𝑘−𝜋 + 𝜋𝑘 ≤ 𝑥 ≤ 𝜋𝑘

{− 𝜋2+ 𝜋𝑘 ≤ 𝑦 ≤𝜋 + 𝜋𝑘2 и {𝜋2 + 𝜋𝑘 ≤ 𝑦 ≤ 3𝜋 2 + 𝜋𝑘 2𝑘 ≤ 𝑥 ≤ 𝜋 − 2𝜋𝑘 −𝜋 − 2𝜋𝑘 ≤ 𝑥 ≤ 2𝜋𝑘

{− 𝜋2 − 2𝜋𝑘 ≤ 𝑦 ≤ 𝜋 − 2𝜋𝑘 2 и {𝜋2 − 2𝜋𝑘 ≤ 𝑦 ≤ 3𝜋 2 − 2𝜋𝑘

4. 𝑧 = 1 + 1 𝑥−𝑦 𝑦 funksiyaning aniqlanish sohasini toping. Найдите область определения функции 𝑧 = 1 + 1. Find the domain of function 𝑧 = 1+ 1.

𝑦 ≠ 𝑥 𝑣𝑎 𝑦 ≠ 0

𝑦 ≠ 𝑥 𝑣𝑎 𝑦 = 0

𝑦 = 𝑥 𝑣𝑎 𝑦 ≠ 0

𝑦 ≠ −𝑥 𝑣𝑎 𝑦 ≠ 0 𝑥−𝑦 𝑦 𝑥−𝑦 𝑦

37. 𝑧 = 𝑥3 + 𝑦2 − 2𝑥𝑦 funksiyaning xususiy hosilalarini toping. Найдите частные производные функции 𝑧 = 𝑥3 + 𝑦2 − 2𝑥𝑦. Find the partial derivatives of a function 𝑧 = 𝑥3 + 𝑦2 − 2𝑥𝑦.

𝑧′ = 3𝑥2 − 2y, 𝑧′ = 2y − 2𝑥 𝑥 𝑦

𝑧′ = 3𝑥2 + 2y, 𝑧′ = 2y − 2𝑥 𝑥 𝑦

𝑧′ = 3𝑥2 − 2y, 𝑧′ = 2y + 2𝑥 𝑥 𝑦

𝑧′ = 3𝑥2 − 2y, 𝑧′ = y − 𝑥 𝑥

42. 𝑢 = √𝑥2 + 𝑦2 funksiyaning xususiy hosilalarini toping. Найдите частные производные функции 𝑢 = √𝑥2 + 𝑦2. Find the partial derivatives of a function 𝑢 = √𝑥2 + 𝑦2.

𝑢′ = 𝑥 , 𝑢′ = 𝑦 𝑥 √𝑥2+𝑦2 𝑦 √𝑥2+𝑦2

𝑢′ = 𝑥 , 𝑢′ = − 𝑦 𝑥 √𝑥2+𝑦2 𝑦 √𝑥2+𝑦2

𝑢′ = − 𝑥 , 𝑢′ = 𝑦 𝑥 √𝑥2+𝑦2 𝑦 √𝑥2+𝑦2

𝑢′ = 2𝑥 , 𝑢′ = 𝑦 𝑥 √𝑥2+𝑦2 𝑦 √𝑥2+𝑦2

математика 1

Authored by Mira Seidakbar

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

𝑧 = 𝑥 + √𝑥𝑦 funksiyaning aniqlanish sohasini toping. Найдите область
2
определения функции 𝑧 = 𝑥 + √𝑥𝑦. Find the domain of function 𝑧 = 𝑥 + √𝑥𝑦.

{𝑥 ≥ 0

𝑦 ≥ 0

𝑣𝑎 {𝑥 ≤ 0

𝑦 ≤ 0

{𝑥 ≥ 0

𝑦 ≥ 0

𝑣𝑎 {𝑥 ≤ 0

𝑦 > 0

{𝑥 ≥ 0

𝑦 ≥ 0

𝑣𝑎 {𝑥 > 0

𝑦 ≤ 0

{𝑥 ≥ 0

𝑦 < 0

𝑣𝑎 {𝑥 ≤ 0

𝑢′ = y, 𝑢′ = 𝑥 + 1

𝑥 𝑦

𝑢′ = y, 𝑢′ = 𝑥 − 1

𝑥 𝑦

𝑢′ = −y, 𝑢′ = 𝑥 + 1

𝑥 𝑦

𝑢′ = y, 𝑢′ = 1

𝑥 𝑦

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математика 1

𝑧 = 𝑥 + √𝑥𝑦 funksiyaning aniqlanish sohasini toping. Найдите область2определения функции 𝑧 = 𝑥 + √𝑥𝑦. Find the domain of function 𝑧 = 𝑥 + √𝑥𝑦.

48. 𝑧 = x𝑦 funksiyaning 𝛛𝛛𝑥 xususiy hosilasini toping. Найдите частную производную 𝛛𝑧𝛛𝑥 функции 𝑧 = x𝑦. Find the partial derivative 𝛛𝛛𝑥 of the function 𝑧 = x𝑦.

47. 𝑧 = 𝑥3 − 𝑦3 funksiyaning 𝛛𝑧𝛛𝑦 xususiy hosilasini toping. Найдите частную производную 𝛛𝑧𝛛𝑦 функции 𝑧 = 𝑥3 − 𝑦3. Find the partial derivative 𝛛𝑧𝛛𝑦 of the function 𝑧 = 𝑥3 − 𝑦3.

44. 𝑢 = 𝑒𝑦𝑥 funksiyaning xususiy hosilalarini toping. Найдите частные производные функции 𝑢 = 𝑒𝑦𝑥. Find the partial derivatives of a function 𝑢 = 𝑒𝑦𝑥.

41. 𝑢 = 𝑥𝑦 + 𝑦 funksiyaning xususiy hosilalarini toping. Найдите частные производные функции 𝑢 = 𝑥𝑦 + 𝑦. Find the partial derivatives of a function𝑢 = 𝑥𝑦 + 𝑦.

40. 𝑧 = ln(𝑥𝑦) funksiyaning xususiy hosilalarini toping. Найдите частные производные функции 𝑧 = ln(𝑥𝑦). Find the partial derivatives of a function𝑧 = ln(𝑥𝑦).

39. 𝑧 = 𝑒−3 funksiyaning xususiy hosilalarini toping. Найдите частные производные𝜋 𝜋функции 𝑧 = 𝑒−3 . Find the partial derivatives of a function 𝑧 = 𝑒−3 .

38. 𝑧 = arctg 𝑥𝑦 𝑦funksiyaning xususiy hosilalarini toping. Найдите частные производные функции 𝑧 = arctg 𝑥. Find the partial derivatives of a function 𝑧 =𝑦 arctg 𝑥.𝑦

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Popular Resources on Wayground

𝑧 = 𝑥 + √𝑥𝑦 funksiyaning aniqlanish sohasini toping. Найдите область
2
определения функции 𝑧 = 𝑥 + √𝑥𝑦. Find the domain of function 𝑧 = 𝑥 + √𝑥𝑦.

48. 𝑧 = x𝑦 funksiyaning 𝛛
𝛛𝑥

xususiy hosilasini toping. Найдите частную

производную 𝛛𝑧
𝛛𝑥

функции 𝑧 = x𝑦. Find the partial derivative 𝛛
𝛛𝑥

of the function

𝑧 = x𝑦.

47. 𝑧 = 𝑥3 − 𝑦3 funksiyaning 𝛛𝑧
𝛛𝑦

xususiy hosilasini toping. Найдите частную

производную 𝛛𝑧
𝛛𝑦

функции 𝑧 = 𝑥3 − 𝑦3. Find the partial derivative 𝛛𝑧
𝛛𝑦

of the function

𝑧 = 𝑥3 − 𝑦3.

41. 𝑢 = 𝑥𝑦 + 𝑦 funksiyaning xususiy hosilalarini toping. Найдите частные производные функции 𝑢 = 𝑥𝑦 + 𝑦. Find the partial derivatives of a function
𝑢 = 𝑥𝑦 + 𝑦.

40. 𝑧 = ln(𝑥𝑦) funksiyaning xususiy hosilalarini toping. Найдите частные производные функции 𝑧 = ln(𝑥𝑦). Find the partial derivatives of a function
𝑧 = ln(𝑥𝑦).

39. 𝑧 = 𝑒−3 funksiyaning xususiy hosilalarini toping. Найдите частные производные
𝜋 𝜋
функции 𝑧 = 𝑒−3 . Find the partial derivatives of a function 𝑧 = 𝑒−3 .

38. 𝑧 = arctg 𝑥
𝑦

𝑦
funksiyaning xususiy hosilalarini toping. Найдите частные

производные функции 𝑧 = arctg 𝑥. Find the partial derivatives of a function 𝑧 =
𝑦

arctg 𝑥.
𝑦