(+mathfrak{F}(2+1)(2^{2}+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1 eching

$$( + \mathfrak { F } ( 2 + 1 ) ( 2 ^ { 2 } + 1 ) ( 2 ^ { 4 } + 1 ) ( 2 ^ { 8 } + 1 ) ( 2 ^ { 16 } + 1 ) ( 2 ^ { 32 } + 1 ) + 1$$

Baholash

$$18446744073709551615F+1$$

Yechim qadamlari

3 olish uchun 2 va 1'ni qo'shing.

$$F\times 3\left(2^{2}+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$F\times 3\left(4+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

5 olish uchun 4 va 1'ni qo'shing.

$$F\times 3\times 5\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

15 hosil qilish uchun 3 va 5 ni ko'paytirish.

$$F\times 15\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

4 daraja ko‘rsatkichini 2 ga hisoblang va 16 ni qiymatni oling.

$$F\times 15\left(16+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

17 olish uchun 16 va 1'ni qo'shing.

$$F\times 15\times 17\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

255 hosil qilish uchun 15 va 17 ni ko'paytirish.

$$F\times 255\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

8 daraja ko‘rsatkichini 2 ga hisoblang va 256 ni qiymatni oling.

$$F\times 255\left(256+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

257 olish uchun 256 va 1'ni qo'shing.

$$F\times 255\times 257\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

65535 hosil qilish uchun 255 va 257 ni ko'paytirish.

$$F\times 65535\left(2^{16}+1\right)\left(2^{32}+1\right)+1$$

16 daraja ko‘rsatkichini 2 ga hisoblang va 65536 ni qiymatni oling.

$$F\times 65535\left(65536+1\right)\left(2^{32}+1\right)+1$$

65537 olish uchun 65536 va 1'ni qo'shing.

$$F\times 65535\times 65537\left(2^{32}+1\right)+1$$

4294967295 hosil qilish uchun 65535 va 65537 ni ko'paytirish.

$$F\times 4294967295\left(2^{32}+1\right)+1$$

32 daraja ko‘rsatkichini 2 ga hisoblang va 4294967296 ni qiymatni oling.

$$F\times 4294967295\left(4294967296+1\right)+1$$

4294967297 olish uchun 4294967296 va 1'ni qo'shing.

$$F\times 4294967295\times 4294967297+1$$

18446744073709551615 hosil qilish uchun 4294967295 va 4294967297 ni ko'paytirish.

$$F\times 18446744073709551615+1$$

F ga nisbatan hosilani topish

$$18446744073709551615$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

3 olish uchun 2 va 1'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 3\left(2^{2}+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 3\left(4+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

5 olish uchun 4 va 1'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 3\times 5\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

15 hosil qilish uchun 3 va 5 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 15\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

4 daraja ko‘rsatkichini 2 ga hisoblang va 16 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 15\left(16+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

17 olish uchun 16 va 1'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 15\times 17\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

255 hosil qilish uchun 15 va 17 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 255\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

8 daraja ko‘rsatkichini 2 ga hisoblang va 256 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 255\left(256+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

257 olish uchun 256 va 1'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 255\times 257\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

65535 hosil qilish uchun 255 va 257 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 65535\left(2^{16}+1\right)\left(2^{32}+1\right)+1)$$

16 daraja ko‘rsatkichini 2 ga hisoblang va 65536 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 65535\left(65536+1\right)\left(2^{32}+1\right)+1)$$

65537 olish uchun 65536 va 1'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 65535\times 65537\left(2^{32}+1\right)+1)$$

4294967295 hosil qilish uchun 65535 va 65537 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 4294967295\left(2^{32}+1\right)+1)$$

32 daraja ko‘rsatkichini 2 ga hisoblang va 4294967296 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 4294967295\left(4294967296+1\right)+1)$$

4294967297 olish uchun 4294967296 va 1'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 4294967295\times 4294967297+1)$$

18446744073709551615 hosil qilish uchun 4294967295 va 4294967297 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}F}(F\times 18446744073709551615+1)$$

Polinomialning hosilasi bu uning shartlari hosilasining yig‘indisiga teng. Konstant shartning hosilasi 0. ax^{n} ning hosilasi nax^{n-1}.

$$18446744073709551615F^{1-1}$$

1 dan 1 ni ayirish.

$$18446744073709551615F^{0}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$18446744073709551615\times 1$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$18446744073709551615$$