(a^5)^2/(a^3)^4 eching

$$\frac { ( a ^ { 5 } ) ^ { 2 } } { ( a ^ { 3 } ) ^ { 4 } }$$

Baholash

$$\frac{1}{a^{2}}$$

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 5 va 2 ni ko‘paytirib, 10 ni oling.

$$\frac{a^{10}}{\left(a^{3}\right)^{4}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 4 ni ko‘paytirib, 12 ni oling.

$$\frac{a^{10}}{a^{12}}$$

a^{12} ni a^{10}a^{2} sifatida qaytadan yozish. Surat va maxrajdagi ikkala a^{10} ni qisqartiring.

$$\frac{1}{a^{2}}$$

a ga nisbatan hosilani topish

$$-\frac{2}{a^{3}}$$

Zanjirli qoidadan foydalanish qadamalari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 5 va 2 ni ko‘paytirib, 10 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{10}}{\left(a^{3}\right)^{4}})$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 4 ni ko‘paytirib, 12 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{10}}{a^{12}})$$

a^{12} ni a^{10}a^{2} sifatida qaytadan yozish. Surat va maxrajdagi ikkala a^{10} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{a^{2}})$$

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.

$$-\left(a^{2}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}a}(a^{2})$$

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

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

Qisqartirish.

$$-2a^{1}\left(a^{2}\right)^{-2}$$

Har qanday t sharti uchun t^{1}=t.

$$-2a\left(a^{2}\right)^{-2}$$