x^-14/x^-2x^-7 eching

$$\frac { x ^ { - 14 } } { x ^ { - 2 } x ^ { - 7 } }$$

Baholash

$$\frac{1}{x^{5}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -2 va -7 ni qo‘shib, -9 ni oling.

$$\frac{x^{-14}}{x^{-9}}$$

x^{-9} ni x^{-14}x^{5} sifatida qaytadan yozish. Surat va maxrajdagi ikkala x^{-14} ni qisqartiring.

$$\frac{1}{x^{5}}$$

x ga nisbatan hosilani topish

$$-\frac{5}{x^{6}}$$

Zanjirli qoidadan foydalanish qadamalari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -2 va -7 ni qo‘shib, -9 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{-14}}{x^{-9}})$$

x^{-9} ni x^{-14}x^{5} sifatida qaytadan yozish. Surat va maxrajdagi ikkala x^{-14} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{5}})$$

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.

$$-\left(x^{5}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{5})$$

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

$$-\left(x^{5}\right)^{-2}\times 5x^{5-1}$$

Qisqartirish.

$$-5x^{4}\left(x^{5}\right)^{-2}$$