10^-63^-7625*x^-4div5^-3*{6}^-5*{x}^-8 eching

$${ 10 }^{ -6 } { 3 }^{ -7 } 625 \times { x }^{ -4 } \div { 5 }^{ -3 } \times { 6 }^{ -5 } \times { x }^{ -8 }$$

Baholash

$$\frac{5}{1088391168x^{12}}$$

Yechim qadamlari

-6 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000000} ni qiymatni oling.

$$\frac{\frac{1}{1000000}\times 3^{-7}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

-7 daraja ko‘rsatkichini 3 ga hisoblang va \frac{1}{2187} ni qiymatni oling.

$$\frac{\frac{1}{1000000}\times \frac{1}{2187}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

\frac{1}{2187000000} hosil qilish uchun \frac{1}{1000000} va \frac{1}{2187} ni ko'paytirish.

$$\frac{\frac{1}{2187000000}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

\frac{1}{3499200} hosil qilish uchun \frac{1}{2187000000} va 625 ni ko'paytirish.

$$\frac{\frac{1}{3499200}x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

-3 daraja ko‘rsatkichini 5 ga hisoblang va \frac{1}{125} ni qiymatni oling.

$$\frac{\frac{1}{3499200}x^{-4}}{\frac{1}{125}}\times 6^{-5}x^{-8}$$

\frac{1}{3499200}x^{-4} ni \frac{1}{125} ga bo'lish \frac{1}{3499200}x^{-4} ga k'paytirish \frac{1}{125} ga qaytarish.

$$\frac{1}{3499200}x^{-4}\times 125\times 6^{-5}x^{-8}$$

\frac{5}{139968} hosil qilish uchun \frac{1}{3499200} va 125 ni ko'paytirish.

$$\frac{5}{139968}x^{-4}\times 6^{-5}x^{-8}$$

-5 daraja ko‘rsatkichini 6 ga hisoblang va \frac{1}{7776} ni qiymatni oling.

$$\frac{5}{139968}x^{-4}\times \frac{1}{7776}x^{-8}$$

\frac{5}{1088391168} hosil qilish uchun \frac{5}{139968} va \frac{1}{7776} ni ko'paytirish.

$$\frac{5}{1088391168}x^{-4}x^{-8}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -4 va -8 ni qo‘shib, -12 ni oling.

$$\frac{5}{1088391168}x^{-12}$$

x ga nisbatan hosilani topish

$$-\frac{5}{90699264x^{13}}$$

Derivativ ifodasidan foydalanish qadamlari

-6 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000000} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{1000000}\times 3^{-7}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

-7 daraja ko‘rsatkichini 3 ga hisoblang va \frac{1}{2187} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{1000000}\times \frac{1}{2187}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

\frac{1}{2187000000} hosil qilish uchun \frac{1}{1000000} va \frac{1}{2187} ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{2187000000}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

\frac{1}{3499200} hosil qilish uchun \frac{1}{2187000000} va 625 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{3499200}x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

-3 daraja ko‘rsatkichini 5 ga hisoblang va \frac{1}{125} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{3499200}x^{-4}}{\frac{1}{125}}\times 6^{-5}x^{-8})$$

\frac{1}{3499200}x^{-4} ni \frac{1}{125} ga bo'lish \frac{1}{3499200}x^{-4} ga k'paytirish \frac{1}{125} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3499200}x^{-4}\times 125\times 6^{-5}x^{-8})$$

\frac{5}{139968} hosil qilish uchun \frac{1}{3499200} va 125 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{139968}x^{-4}\times 6^{-5}x^{-8})$$

-5 daraja ko‘rsatkichini 6 ga hisoblang va \frac{1}{7776} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{139968}x^{-4}\times \frac{1}{7776}x^{-8})$$

\frac{5}{1088391168} hosil qilish uchun \frac{5}{139968} va \frac{1}{7776} ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{1088391168}x^{-4}x^{-8})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -4 va -8 ni qo‘shib, -12 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{1088391168}x^{-12})$$

ax^{n} hosilasi – nax^{n-1}.

$$-12\times \frac{5}{1088391168}x^{-12-1}$$

-12 ni \frac{5}{1088391168} marotabaga ko'paytirish.

$$-\frac{5}{90699264}x^{-12-1}$$

-12 dan 1 ni ayirish.

$$-\frac{5}{90699264}x^{-13}$$