1/a+1/a-1{a+frac{1/a}} eching

$$\frac { \frac { 1 } { a + 1 } } { a - \frac { 1 } { a + \frac { 1 } { a } } }$$

Baholash

$$\frac{a^{2}+1}{\left(a+1\right)a^{3}}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. a ni \frac{a}{a} marotabaga ko'paytirish.

$$\frac{\frac{1}{a+1}}{a-\frac{1}{\frac{aa}{a}+\frac{1}{a}}}$$

\frac{aa}{a} va \frac{1}{a} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{1}{a+1}}{a-\frac{1}{\frac{aa+1}{a}}}$$

aa+1 ichidagi ko‘paytirishlarni bajaring.

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

1 ni \frac{a^{2}+1}{a} ga bo'lish 1 ga k'paytirish \frac{a^{2}+1}{a} ga qaytarish.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. a ni \frac{a^{2}+1}{a^{2}+1} marotabaga ko'paytirish.

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

\frac{a\left(a^{2}+1\right)}{a^{2}+1} va \frac{a}{a^{2}+1} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

a\left(a^{2}+1\right)-a ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{1}{a+1}}{\frac{a^{3}+a-a}{a^{2}+1}}$$

a^{3}+a-a kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{1}{a+1}}{\frac{a^{3}}{a^{2}+1}}$$

\frac{1}{a+1} ni \frac{a^{3}}{a^{2}+1} ga bo'lish \frac{1}{a+1} ga k'paytirish \frac{a^{3}}{a^{2}+1} ga qaytarish.

$$\frac{a^{2}+1}{\left(a+1\right)a^{3}}$$

a+1 ga a^{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{a^{2}+1}{a^{4}+a^{3}}$$

a ga nisbatan hosilani topish

$$-\frac{2a^{3}+a^{2}+4a+3}{\left(a+1\right)^{2}a^{4}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. a ni \frac{a}{a} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{a+1}}{a-\frac{1}{\frac{aa}{a}+\frac{1}{a}}})$$

\frac{aa}{a} va \frac{1}{a} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{a+1}}{a-\frac{1}{\frac{aa+1}{a}}})$$

aa+1 ichidagi ko‘paytirishlarni bajaring.

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

1 ni \frac{a^{2}+1}{a} ga bo'lish 1 ga k'paytirish \frac{a^{2}+1}{a} ga qaytarish.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. a ni \frac{a^{2}+1}{a^{2}+1} marotabaga ko'paytirish.

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

\frac{a\left(a^{2}+1\right)}{a^{2}+1} va \frac{a}{a^{2}+1} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

a\left(a^{2}+1\right)-a ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{a+1}}{\frac{a^{3}+a-a}{a^{2}+1}})$$

a^{3}+a-a kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{a+1}}{\frac{a^{3}}{a^{2}+1}})$$

\frac{1}{a+1} ni \frac{a^{3}}{a^{2}+1} ga bo'lish \frac{1}{a+1} ga k'paytirish \frac{a^{3}}{a^{2}+1} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{2}+1}{\left(a+1\right)a^{3}})$$

a+1 ga a^{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{2}+1}{a^{4}+a^{3}})$$

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

$$\frac{\left(a^{4}+a^{3}\right)\frac{\mathrm{d}}{\mathrm{d}a}(a^{2}+1)-\left(a^{2}+1\right)\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}+a^{3})}{\left(a^{4}+a^{3}\right)^{2}}$$

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

$$\frac{\left(a^{4}+a^{3}\right)\times 2a^{2-1}-\left(a^{2}+1\right)\left(4a^{4-1}+3a^{3-1}\right)}{\left(a^{4}+a^{3}\right)^{2}}$$

Qisqartirish.

$$\frac{\left(a^{4}+a^{3}\right)\times 2a^{1}-\left(a^{2}+1\right)\left(4a^{3}+3a^{2}\right)}{\left(a^{4}+a^{3}\right)^{2}}$$

a^{4}+a^{3} ni 2a^{1} marotabaga ko'paytirish.

$$\frac{a^{4}\times 2a^{1}+a^{3}\times 2a^{1}-\left(a^{2}+1\right)\left(4a^{3}+3a^{2}\right)}{\left(a^{4}+a^{3}\right)^{2}}$$

a^{2}+1 ni 4a^{3}+3a^{2} marotabaga ko'paytirish.

$$\frac{a^{4}\times 2a^{1}+a^{3}\times 2a^{1}-\left(a^{2}\times 4a^{3}+a^{2}\times 3a^{2}+4a^{3}+3a^{2}\right)}{\left(a^{4}+a^{3}\right)^{2}}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$\frac{2a^{4+1}+2a^{3+1}-\left(4a^{2+3}+3a^{2+2}+4a^{3}+3a^{2}\right)}{\left(a^{4}+a^{3}\right)^{2}}$$

Qisqartirish.

$$\frac{2a^{5}+2a^{4}-\left(4a^{5}+3a^{4}+4a^{3}+3a^{2}\right)}{\left(a^{4}+a^{3}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-2a^{5}-a^{4}-4a^{3}-3a^{2}}{\left(a^{4}+a^{3}\right)^{2}}$$