(1+x)(1-x)(1+x^2x(+x^4) eching

$$( 1 + x ) ( 1 - x ) ( 1 + x ^ { 2 } x ( + x ^ { 4 } )$$

Baholash

$$\left(1-x^{2}\right)\left(x^{7}+1\right)$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\left(1+x\right)\left(1-x\right)\left(1+x^{3}x^{4}\right)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 4 ni qo‘shib, 7 ni oling.

$$\left(1+x\right)\left(1-x\right)\left(1+x^{7}\right)$$

1+x ga 1-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\left(1-x^{2}\right)\left(1+x^{7}\right)$$

1-x^{2} ga 1+x^{7} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1+x^{7}-x^{2}-x^{9}$$

x ga nisbatan hosilani topish

$$x\left(-9x^{7}+7x^{5}-2\right)$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(1+x\right)\left(1-x\right)\left(1+x^{3}x^{4}\right))$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 4 ni qo‘shib, 7 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(1+x\right)\left(1-x\right)\left(1+x^{7}\right))$$

1+x ga 1-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(1-x^{2}\right)\left(1+x^{7}\right))$$

1-x^{2} ga 1+x^{7} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1+x^{7}-x^{2}-x^{9})$$

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

$$7x^{7-1}+2\left(-1\right)x^{2-1}+9\left(-1\right)x^{9-1}$$

7 dan 1 ni ayirish.

$$7x^{6}+2\left(-1\right)x^{2-1}+9\left(-1\right)x^{9-1}$$

2 ni -1 marotabaga ko'paytirish.

$$7x^{6}-2x^{2-1}+9\left(-1\right)x^{9-1}$$

2 dan 1 ni ayirish.

$$7x^{6}-2x^{1}+9\left(-1\right)x^{9-1}$$

2 ni -1 marotabaga ko'paytirish.

$$7x^{6}-2x^{1}-9x^{9-1}$$

9 dan 1 ni ayirish.

$$7x^{6}-2x^{1}-9x^{8}$$

Har qanday t sharti uchun t^{1}=t.

$$7x^{6}-2x-9x^{8}$$