m:(-1/2)^3*sqrt{25/9}*sqrt{(8/5)^2}*3^-1= eching

$$m : ( - \frac { 1 } { 2 } ) ^ { 3 } \times \sqrt { \frac { 25 } { 9 } } \times \sqrt { ( \frac { 8 } { 5 } ) ^ { 2 } } \times 3 ^ { - 1 } =$$

Baholash

$$-\frac{64m}{9}$$

Yechim qadamlari

3 daraja ko‘rsatkichini -\frac{1}{2} ga hisoblang va -\frac{1}{8} ni qiymatni oling.

$$\frac{m}{-\frac{1}{8}}\sqrt{\frac{25}{9}}\sqrt{\left(\frac{8}{5}\right)^{2}}\times 3^{-1}$$

m ni -\frac{1}{8} ga bo'lish m ga k'paytirish -\frac{1}{8} ga qaytarish.

$$\frac{m\times 8}{-1}\sqrt{\frac{25}{9}}\sqrt{\left(\frac{8}{5}\right)^{2}}\times 3^{-1}$$

Istalgan sonni -1 ga boʻlsangiz, uning qarama-qarshisi chiqadi.

$$\left(-m\times 8\right)\sqrt{\frac{25}{9}}\sqrt{\left(\frac{8}{5}\right)^{2}}\times 3^{-1}$$

\frac{25}{9} boʻlinmasining kvadrat ildizini \frac{\sqrt{25}}{\sqrt{9}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\left(-m\times 8\right)\times \frac{5}{3}\sqrt{\left(\frac{8}{5}\right)^{2}}\times 3^{-1}$$

2 daraja ko‘rsatkichini \frac{8}{5} ga hisoblang va \frac{64}{25} ni qiymatni oling.

$$\left(-m\times 8\right)\times \frac{5}{3}\sqrt{\frac{64}{25}}\times 3^{-1}$$

\frac{64}{25} boʻlinmasining kvadrat ildizini \frac{\sqrt{64}}{\sqrt{25}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\left(-m\times 8\right)\times \frac{5}{3}\times \frac{8}{5}\times 3^{-1}$$

\frac{8}{3} hosil qilish uchun \frac{5}{3} va \frac{8}{5} ni ko'paytirish.

$$\left(-m\times 8\right)\times \frac{8}{3}\times 3^{-1}$$

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

$$\left(-m\times 8\right)\times \frac{8}{3}\times \frac{1}{3}$$

\frac{8}{9} hosil qilish uchun \frac{8}{3} va \frac{1}{3} ni ko'paytirish.

$$\left(-m\times 8\right)\times \frac{8}{9}$$

-8 hosil qilish uchun -1 va 8 ni ko'paytirish.

$$-8m\times \frac{8}{9}$$

-\frac{64}{9} hosil qilish uchun -8 va \frac{8}{9} ni ko'paytirish.

$$-\frac{64}{9}m$$

m ga nisbatan hosilani topish

$$-\frac{64}{9} = -7\frac{1}{9} = -7,111111111111111$$

Derivativ ifodasidan foydalanish qadamlari

3 daraja ko‘rsatkichini -\frac{1}{2} ga hisoblang va -\frac{1}{8} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m}{-\frac{1}{8}}\sqrt{\frac{25}{9}}\sqrt{\left(\frac{8}{5}\right)^{2}}\times 3^{-1})$$

m ni -\frac{1}{8} ga bo'lish m ga k'paytirish -\frac{1}{8} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m\times 8}{-1}\sqrt{\frac{25}{9}}\sqrt{\left(\frac{8}{5}\right)^{2}}\times 3^{-1})$$

Istalgan sonni -1 ga boʻlsangiz, uning qarama-qarshisi chiqadi.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-m\times 8\right)\sqrt{\frac{25}{9}}\sqrt{\left(\frac{8}{5}\right)^{2}}\times 3^{-1})$$

\frac{25}{9} boʻlinmasining kvadrat ildizini \frac{\sqrt{25}}{\sqrt{9}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-m\times 8\right)\times \frac{5}{3}\sqrt{\left(\frac{8}{5}\right)^{2}}\times 3^{-1})$$

2 daraja ko‘rsatkichini \frac{8}{5} ga hisoblang va \frac{64}{25} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-m\times 8\right)\times \frac{5}{3}\sqrt{\frac{64}{25}}\times 3^{-1})$$

\frac{64}{25} boʻlinmasining kvadrat ildizini \frac{\sqrt{64}}{\sqrt{25}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-m\times 8\right)\times \frac{5}{3}\times \frac{8}{5}\times 3^{-1})$$

\frac{8}{3} hosil qilish uchun \frac{5}{3} va \frac{8}{5} ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-m\times 8\right)\times \frac{8}{3}\times 3^{-1})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-m\times 8\right)\times \frac{8}{3}\times \frac{1}{3})$$

\frac{8}{9} hosil qilish uchun \frac{8}{3} va \frac{1}{3} ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(-m\times 8\right)\times \frac{8}{9})$$

-8 hosil qilish uchun -1 va 8 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-8m\times \frac{8}{9})$$

-\frac{64}{9} hosil qilish uchun -8 va \frac{8}{9} ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-\frac{64}{9}m)$$

ax^{n} hosilasi – nax^{n-1}.

$$-\frac{64}{9}m^{1-1}$$

1 dan 1 ni ayirish.

$$-\frac{64}{9}m^{0}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$-\frac{64}{9}$$