(-r^4/64r^7)^frac{2{3}} eching

$$( \frac { - r ^ { 4 } } { 64 r ^ { 7 } } ) ^ { \frac { 2 } { 3 } }$$

Baholash

$$\frac{1}{16r^{2}}$$

Yechim qadamlari

\frac{-r^{4}}{64r^{7}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(-r^{4}\right)^{\frac{2}{3}}}{\left(64r^{7}\right)^{\frac{2}{3}}}$$

\left(64r^{7}\right)^{\frac{2}{3}} ni kengaytirish.

$$\frac{\left(-r^{4}\right)^{\frac{2}{3}}}{64^{\frac{2}{3}}\left(r^{7}\right)^{\frac{2}{3}}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 7 va \frac{2}{3} ni ko‘paytirib, \frac{14}{3} ni oling.

$$\frac{\left(-r^{4}\right)^{\frac{2}{3}}}{64^{\frac{2}{3}}r^{\frac{14}{3}}}$$

\frac{2}{3} daraja ko‘rsatkichini 64 ga hisoblang va 16 ni qiymatni oling.

$$\frac{\left(-r^{4}\right)^{\frac{2}{3}}}{16r^{\frac{14}{3}}}$$

\left(-r^{4}\right)^{\frac{2}{3}} ni kengaytirish.

$$\frac{\left(-1\right)^{\frac{2}{3}}\left(r^{4}\right)^{\frac{2}{3}}}{16r^{\frac{14}{3}}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va \frac{2}{3} ni ko‘paytirib, \frac{8}{3} ni oling.

$$\frac{\left(-1\right)^{\frac{2}{3}}r^{\frac{8}{3}}}{16r^{\frac{14}{3}}}$$

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

$$\frac{1r^{\frac{8}{3}}}{16r^{\frac{14}{3}}}$$

Surat va maxrajdagi ikkala r^{\frac{8}{3}} ni qisqartiring.

$$\frac{1}{16r^{2}}$$

r ga nisbatan hosilani topish

$$-\frac{1}{8r^{3}}$$

Zanjirli qoidadan foydalanish qadamalari

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.

$$\frac{2}{3}\times \left(\frac{-r^{4}}{64r^{7}}\right)^{\frac{2}{3}-1}\frac{\mathrm{d}}{\mathrm{d}r}(\frac{-r^{4}}{64r^{7}})$$

Har qanday ikki differensial funksiya uchun ikki funksiyaning koeffitsient hosilasi raqamlagichning hosila marotabasi maxraj minusi va barchasi kvadrat maxrajiga bo'lingan.

$$\frac{\frac{2}{3}\times \left(\frac{-r^{4}}{64r^{7}}\right)^{\frac{2}{3}-1}\left(64r^{7}\frac{\mathrm{d}}{\mathrm{d}r}(-r^{4})-\left(-r^{4}\frac{\mathrm{d}}{\mathrm{d}r}(64r^{7})\right)\right)}{\left(64r^{7}\right)^{2}}$$

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

$$\frac{\frac{2}{3}\times \left(\frac{-r^{4}}{64r^{7}}\right)^{\frac{2}{3}-1}\left(64r^{7}\times 4\left(-1\right)r^{4-1}-\left(-r^{4}\times 7\times 64r^{7-1}\right)\right)}{\left(64r^{7}\right)^{2}}$$

64r^{7} ni 4\left(-1\right)r^{4-1} marotabaga ko'paytirish.

$$\frac{\frac{2}{3}\times \left(\frac{-r^{4}}{64r^{7}}\right)^{-\frac{1}{3}}\left(-256r^{7}r^{3}-\left(-r^{4}\times 7\times 64r^{7-1}\right)\right)}{\left(64r^{7}\right)^{2}}$$

-r^{4} ni 7\times 64r^{7-1} marotabaga ko'paytirish.

$$\frac{\frac{2}{3}\times \left(\frac{-r^{4}}{64r^{7}}\right)^{-\frac{1}{3}}\left(-256r^{10}-\left(-448r^{4}r^{6}\right)\right)}{\left(64r^{7}\right)^{2}}$$

Qisqartirish.

$$\frac{\frac{2}{3}\times \left(\frac{-r^{4}}{64r^{7}}\right)^{-\frac{1}{3}}\left(-256r^{10}-\left(-448r^{10}\right)\right)}{\left(64r^{7}\right)^{2}}$$