(1/2-1/4-1/6)x^12-25frac{5{6}}div(-5) eching

$$( \frac { 1 } { 2 } - \frac { 1 } { 4 } - \frac { 1 } { 6 } ) x ^ { 12 - 25 \frac { 5 } { 6 } } \div ( - 5 )$$

Baholash

$$-\frac{1}{60x^{\frac{83}{6}}}$$

Yechim qadamlari

\frac{1}{4} olish uchun \frac{1}{2} dan \frac{1}{4} ni ayirish.

$$\frac{\left(\frac{1}{4}-\frac{1}{6}\right)x^{12-\frac{25\times 6+5}{6}}}{-5}$$

\frac{1}{12} olish uchun \frac{1}{4} dan \frac{1}{6} ni ayirish.

$$\frac{\frac{1}{12}x^{12-\frac{25\times 6+5}{6}}}{-5}$$

150 hosil qilish uchun 25 va 6 ni ko'paytirish.

$$\frac{\frac{1}{12}x^{12-\frac{150+5}{6}}}{-5}$$

155 olish uchun 150 va 5'ni qo'shing.

$$\frac{\frac{1}{12}x^{12-\frac{155}{6}}}{-5}$$

-\frac{83}{6} olish uchun 12 dan \frac{155}{6} ni ayirish.

$$\frac{\frac{1}{12}x^{-\frac{83}{6}}}{-5}$$

-\frac{1}{60}x^{-\frac{83}{6}} ni olish uchun \frac{1}{12}x^{-\frac{83}{6}} ni -5 ga bo‘ling.

$$-\frac{1}{60}x^{-\frac{83}{6}}$$

x ga nisbatan hosilani topish

$$\frac{83}{360x^{\frac{89}{6}}}$$

Derivativ ifodasidan foydalanish qadamlari

\frac{1}{4} olish uchun \frac{1}{2} dan \frac{1}{4} ni ayirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(\frac{1}{4}-\frac{1}{6}\right)x^{12-\frac{25\times 6+5}{6}}}{-5})$$

\frac{1}{12} olish uchun \frac{1}{4} dan \frac{1}{6} ni ayirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{12}x^{12-\frac{25\times 6+5}{6}}}{-5})$$

150 hosil qilish uchun 25 va 6 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{12}x^{12-\frac{150+5}{6}}}{-5})$$

155 olish uchun 150 va 5'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{12}x^{12-\frac{155}{6}}}{-5})$$

-\frac{83}{6} olish uchun 12 dan \frac{155}{6} ni ayirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{12}x^{-\frac{83}{6}}}{-5})$$

-\frac{1}{60}x^{-\frac{83}{6}} ni olish uchun \frac{1}{12}x^{-\frac{83}{6}} ni -5 ga bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{60}x^{-\frac{83}{6}})$$

ax^{n} hosilasi – nax^{n-1}.

$$-\frac{83}{6}\left(-\frac{1}{60}\right)x^{-\frac{83}{6}-1}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali -\frac{83}{6} ni -\frac{1}{60} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$\frac{83}{360}x^{-\frac{83}{6}-1}$$

-\frac{83}{6} dan 1 ni ayirish.

$$\frac{83}{360}x^{-\frac{89}{6}}$$