d/dyleft(1-1/y^5right) eching

$$\frac{d}{d y } \left(1- \frac{ 1 }{ { y }^{ 5 } } \right)$$

Baholash

$$\frac{5}{y^{6}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{y^{5}}{y^{5}} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{5}}{y^{5}}-\frac{1}{y^{5}})$$

\frac{y^{5}}{y^{5}} va \frac{1}{y^{5}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{5}-1}{y^{5}})$$

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

$$\frac{y^{5}\frac{\mathrm{d}}{\mathrm{d}y}(y^{5}-1)-\left(y^{5}-1\right)\frac{\mathrm{d}}{\mathrm{d}y}(y^{5})}{\left(y^{5}\right)^{2}}$$

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

$$\frac{y^{5}\times 5y^{5-1}-\left(y^{5}-1\right)\times 5y^{5-1}}{\left(y^{5}\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{y^{5}\times 5y^{4}-\left(y^{5}-1\right)\times 5y^{4}}{\left(y^{5}\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{y^{5}\times 5y^{4}-\left(y^{5}\times 5y^{4}-5y^{4}\right)}{\left(y^{5}\right)^{2}}$$

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{5y^{9}-\left(5y^{9}-5y^{4}\right)}{\left(y^{5}\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{5y^{9}-5y^{9}-\left(-5y^{4}\right)}{\left(y^{5}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(5-5\right)y^{9}+\left(-\left(-5\right)\right)y^{4}}{\left(y^{5}\right)^{2}}$$

5 dan 5 ni ayirish.

$$-\frac{-5y^{4}}{\left(y^{5}\right)^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring.

$$-\frac{-5y^{4}}{y^{5\times 2}}$$

5 ni 2 marotabaga ko'paytirish.

$$\frac{\left(-\left(-5\right)\right)y^{4}}{y^{10}}$$

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\left(-\frac{-5}{1}\right)y^{4-10}$$

Arifmetik hisobni amalga oshirish.

$$5y^{-6}$$

y ga nisbatan hosilani topish

$$-\frac{30}{y^{7}}$$