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

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

मूल्यांकन करचें

$$18446744073709551615F+1$$

सोडोवणी पांवडे

3 मेळोवंक 2 आनी 1 ची बेरीज करची.

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

4 मेळोवंक 2 चो 2 पॉवर मेजचो.

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

5 मेळोवंक 4 आनी 1 ची बेरीज करची.

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

15 मेळोवंक 3 आनी 5 गुणचें.

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

16 मेळोवंक 4 चो 2 पॉवर मेजचो.

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

17 मेळोवंक 16 आनी 1 ची बेरीज करची.

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

255 मेळोवंक 15 आनी 17 गुणचें.

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

256 मेळोवंक 8 चो 2 पॉवर मेजचो.

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

257 मेळोवंक 256 आनी 1 ची बेरीज करची.

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

65535 मेळोवंक 255 आनी 257 गुणचें.

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

65536 मेळोवंक 16 चो 2 पॉवर मेजचो.

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

65537 मेळोवंक 65536 आनी 1 ची बेरीज करची.

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

4294967295 मेळोवंक 65535 आनी 65537 गुणचें.

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

4294967296 मेळोवंक 32 चो 2 पॉवर मेजचो.

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

4294967297 मेळोवंक 4294967296 आनी 1 ची बेरीज करची.

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

18446744073709551615 मेळोवंक 4294967295 आनी 4294967297 गुणचें.

$$F\times 18446744073709551615+1$$

w.r.t. F चो फरक काडचो

$$18446744073709551615$$

बेरीज खातीर व्यत्पन्न नेम वापरून पांवडे

3 मेळोवंक 2 आनी 1 ची बेरीज करची.

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

4 मेळोवंक 2 चो 2 पॉवर मेजचो.

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

5 मेळोवंक 4 आनी 1 ची बेरीज करची.

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

15 मेळोवंक 3 आनी 5 गुणचें.

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

16 मेळोवंक 4 चो 2 पॉवर मेजचो.

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

17 मेळोवंक 16 आनी 1 ची बेरीज करची.

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

255 मेळोवंक 15 आनी 17 गुणचें.

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

256 मेळोवंक 8 चो 2 पॉवर मेजचो.

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

257 मेळोवंक 256 आनी 1 ची बेरीज करची.

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

65535 मेळोवंक 255 आनी 257 गुणचें.

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

65536 मेळोवंक 16 चो 2 पॉवर मेजचो.

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

65537 मेळोवंक 65536 आनी 1 ची बेरीज करची.

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

4294967295 मेळोवंक 65535 आनी 65537 गुणचें.

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

4294967296 मेळोवंक 32 चो 2 पॉवर मेजचो.

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

4294967297 मेळोवंक 4294967296 आनी 1 ची बेरीज करची.

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

18446744073709551615 मेळोवंक 4294967295 आनी 4294967297 गुणचें.

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

पोलिनोमियलाचें व्यत्पन्न हें तांच्या संज्ञांच्या व्यत्पन्नाची बेरीज आसता. खंयच्याय थीर संख्येचें व्यत्पन्न 0 आसता. हाचें व्यत्पन्न ax^{n} हें nax^{n-1} आसा.

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

1 तल्यान 1 वजा करची.

$$18446744073709551615F^{0}$$

0 सोडून t खंयच्याय शब्दा खातीर, t^{0}=1.

$$18446744073709551615\times 1$$

t खंयच्याय शब्दा खातीर, t\times 1=t आनी 1t=t .

$$18446744073709551615$$