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

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

Avaliar

$$18446744073709551615F+1$$

Passos Para a Resolução

Some 2 e 1 para obter 3.

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

Calcule 2 elevado a 2 e obtenha 4.

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

Some 4 e 1 para obter 5.

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

Multiplique 3 e 5 para obter 15.

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

Calcule 2 elevado a 4 e obtenha 16.

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

Some 16 e 1 para obter 17.

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

Multiplique 15 e 17 para obter 255.

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

Calcule 2 elevado a 8 e obtenha 256.

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

Some 256 e 1 para obter 257.

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

Multiplique 255 e 257 para obter 65535.

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

Calcule 2 elevado a 16 e obtenha 65536.

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

Some 65536 e 1 para obter 65537.

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

Multiplique 65535 e 65537 para obter 4294967295.

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

Calcule 2 elevado a 32 e obtenha 4294967296.

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

Some 4294967296 e 1 para obter 4294967297.

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

Multiplique 4294967295 e 4294967297 para obter 18446744073709551615.

$$F\times 18446744073709551615+1$$

Calcular a diferenciação com respeito a F

$$18446744073709551615$$

Passos Para Utilizar a Regra de Derivação da Soma

Some 2 e 1 para obter 3.

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

Calcule 2 elevado a 2 e obtenha 4.

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

Some 4 e 1 para obter 5.

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

Multiplique 3 e 5 para obter 15.

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

Calcule 2 elevado a 4 e obtenha 16.

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

Some 16 e 1 para obter 17.

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

Multiplique 15 e 17 para obter 255.

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

Calcule 2 elevado a 8 e obtenha 256.

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

Some 256 e 1 para obter 257.

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

Multiplique 255 e 257 para obter 65535.

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

Calcule 2 elevado a 16 e obtenha 65536.

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

Some 65536 e 1 para obter 65537.

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

Multiplique 65535 e 65537 para obter 4294967295.

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

Calcule 2 elevado a 32 e obtenha 4294967296.

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

Some 4294967296 e 1 para obter 4294967297.

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

Multiplique 4294967295 e 4294967297 para obter 18446744073709551615.

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

A derivada de um polinómio é a soma das derivadas dos seus termos. A derivada de qualquer termo constante é 0. A derivada de ax^{n} é nax^{n-1}.

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

Subtraia 1 de 1.

$$18446744073709551615F^{0}$$

Para qualquer termo t , exceto 0, t^{0}=1.

$$18446744073709551615\times 1$$

Para qualquer termo t, t\times 1=t e 1t=t.

$$18446744073709551615$$