(x^2)^4/x^20= eching

$$\frac { ( x ^ { 2 } ) ^ { 4 } } { x ^ { 20 } } =$$

Baholash

$$\frac{1}{x^{12}}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(x^{2}\right)^{4}\times \frac{1}{x^{20}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring.

$$x^{2\times 4}x^{20\left(-1\right)}$$

2 ni 4 marotabaga ko'paytirish.

$$x^{8}x^{20\left(-1\right)}$$

20 ni -1 marotabaga ko'paytirish.

$$x^{8}x^{-20}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$x^{8-20}$$

8 va -20 belgilarini qo'shish.

$$x^{-12}$$

x ga nisbatan hosilani topish

$$-\frac{12}{x^{13}}$$

Zanjirli qoidadan foydalanish qadamalari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 4 ni ko‘paytirib, 8 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{8}}{x^{20}})$$

x^{20} ni x^{8}x^{12} sifatida qaytadan yozish. Surat va maxrajdagi ikkala x^{8} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{12}})$$

Agar F ikki differensial funksiya f\left(u\right) va u=g\left(x\right)'ning yig'indisi bo'lsa, ya'ni agar F\left(x\right)=f\left(g\left(x\right)\right) bo'lsa, F hosilasi f'ning u martalik hosilasi, g'ning x martalik hosilasi ya'ni \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right) bo'ladi.

$$-\left(x^{12}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{12})$$

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

$$-\left(x^{12}\right)^{-2}\times 12x^{12-1}$$

Qisqartirish.

$$-12x^{11}\left(x^{12}\right)^{-2}$$