x^3y^5/3x*y^4/x^2 eching

$$\frac{x^3y^5}{3x} \times \frac{y^4}{x^2}$$

Baholash

$$\frac{y^{9}}{3}$$

Yechim qadamlari

Surat va maxrajdagi ikkala x ni qisqartiring.

$$\frac{x^{2}y^{5}}{3}\times \frac{y^{4}}{x^{2}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x^{2}y^{5}}{3} ni \frac{y^{4}}{x^{2}} ga ko‘paytiring.

$$\frac{x^{2}y^{5}y^{4}}{3x^{2}}$$

Surat va maxrajdagi ikkala x^{2} ni qisqartiring.

$$\frac{y^{4}y^{5}}{3}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 5 ni qo‘shib, 9 ni oling.

$$\frac{y^{9}}{3}$$

y ga nisbatan hosilani topish

$$3y^{8}$$

Derivativ ifodasidan foydalanish qadamlari

Surat va maxrajdagi ikkala x ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{x^{2}y^{5}}{3}\times \frac{y^{4}}{x^{2}})$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x^{2}y^{5}}{3} ni \frac{y^{4}}{x^{2}} ga ko‘paytiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{x^{2}y^{5}y^{4}}{3x^{2}})$$

Surat va maxrajdagi ikkala x^{2} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{4}y^{5}}{3})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 5 ni qo‘shib, 9 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{9}}{3})$$

ax^{n} hosilasi – nax^{n-1}.

$$9\times \frac{1}{3}y^{9-1}$$

9 ni \frac{1}{3} marotabaga ko'paytirish.

$$3y^{9-1}$$

9 dan 1 ni ayirish.

$$3y^{8}$$