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

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

Evalwa

$$18446744073709551615F+1$$

Passi tas-Soluzzjonijiet

Żid 2 u 1 biex tikseb 3.

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

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

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

Żid 4 u 1 biex tikseb 5.

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

Immultiplika 3 u 5 biex tikseb 15.

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

Ikkalkula 2 bil-power ta' 4 u tikseb 16.

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

Żid 16 u 1 biex tikseb 17.

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

Immultiplika 15 u 17 biex tikseb 255.

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

Ikkalkula 2 bil-power ta' 8 u tikseb 256.

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

Żid 256 u 1 biex tikseb 257.

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

Immultiplika 255 u 257 biex tikseb 65535.

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

Ikkalkula 2 bil-power ta' 16 u tikseb 65536.

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

Żid 65536 u 1 biex tikseb 65537.

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

Immultiplika 65535 u 65537 biex tikseb 4294967295.

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

Ikkalkula 2 bil-power ta' 32 u tikseb 4294967296.

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

Żid 4294967296 u 1 biex tikseb 4294967297.

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

Immultiplika 4294967295 u 4294967297 biex tikseb 18446744073709551615.

$$F\times 18446744073709551615+1$$

Iddifferenzja w.r.t. F

$$18446744073709551615$$

Passi għall-Użu ta' Regola Derivattiva għal Somma

Żid 2 u 1 biex tikseb 3.

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

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

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

Żid 4 u 1 biex tikseb 5.

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

Immultiplika 3 u 5 biex tikseb 15.

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

Ikkalkula 2 bil-power ta' 4 u tikseb 16.

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

Żid 16 u 1 biex tikseb 17.

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

Immultiplika 15 u 17 biex tikseb 255.

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

Ikkalkula 2 bil-power ta' 8 u tikseb 256.

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

Żid 256 u 1 biex tikseb 257.

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

Immultiplika 255 u 257 biex tikseb 65535.

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

Ikkalkula 2 bil-power ta' 16 u tikseb 65536.

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

Żid 65536 u 1 biex tikseb 65537.

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

Immultiplika 65535 u 65537 biex tikseb 4294967295.

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

Ikkalkula 2 bil-power ta' 32 u tikseb 4294967296.

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

Żid 4294967296 u 1 biex tikseb 4294967297.

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

Immultiplika 4294967295 u 4294967297 biex tikseb 18446744073709551615.

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

Id-derivattiva ta’ polynomial hija s-somma tad-derivattivi tat-termini tagħha. Id-derivattiva ta’ terminu kostanti hija 0. Id-derivattiva ta’ ax^{n} hijanax^{n-1}.

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

Naqqas 1 minn 1.

$$18446744073709551615F^{0}$$

Għal kwalunkwe terminu t ħlief 0, t^{0}=1.

$$18446744073709551615\times 1$$

Għal kwalunkwe terminu t, t\times 1=t u 1t=t.

$$18446744073709551615$$