x^6(x^-3/x^-10)^-1 eching

$$x ^ { 6 } ( x ^ { - 3 } / x ^ { - 10 } ) ^ { - 1 }$$

Baholash

$$\frac{1}{x}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. -3 dan -10 ni ayirib, 7 ni oling.

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 7 va -1 ni ko‘paytirib, -7 ni oling.

$$x^{6}x^{-7}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 6 va -7 ni qo‘shib, -1 ni oling.

$$x^{-1}$$

x ga nisbatan hosilani topish

$$-\frac{1}{x^{2}}$$

Derivativ ifodasidan foydalanish qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. -3 dan -10 ni ayirib, 7 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}\left(x^{7}\right)^{-1})$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 7 va -1 ni ko‘paytirib, -7 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}x^{-7})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 6 va -7 ni qo‘shib, -1 ni oling.

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

ax^{n} hosilasi – nax^{n-1}.

$$-x^{-1-1}$$

-1 dan 1 ni ayirish.

$$-x^{-2}$$