5/6x7/10x5/34x38/75 eching

$$\frac { 5 } { 6 } x \frac { 7 } { 10 } x \frac { 5 } { 34 } x \frac { 38 } { 75 }$$

Baholash

$$\frac{133x^{3}}{3060}$$

Yechim qadamlari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\frac{5}{6}x^{2}\times \frac{7}{10}\times \frac{5}{34}x\times \frac{38}{75}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\frac{5}{6}x^{3}\times \frac{7}{10}\times \frac{5}{34}\times \frac{38}{75}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{6} ni \frac{7}{10} ga ko‘paytiring.

$$\frac{5\times 7}{6\times 10}x^{3}\times \frac{5}{34}\times \frac{38}{75}$$

\frac{5\times 7}{6\times 10} kasridagi ko‘paytirishlarni bajaring.

$$\frac{35}{60}x^{3}\times \frac{5}{34}\times \frac{38}{75}$$

\frac{35}{60} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{7}{12}x^{3}\times \frac{5}{34}\times \frac{38}{75}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{7}{12} ni \frac{5}{34} ga ko‘paytiring.

$$\frac{7\times 5}{12\times 34}x^{3}\times \frac{38}{75}$$

\frac{7\times 5}{12\times 34} kasridagi ko‘paytirishlarni bajaring.

$$\frac{35}{408}x^{3}\times \frac{38}{75}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{35}{408} ni \frac{38}{75} ga ko‘paytiring.

$$\frac{35\times 38}{408\times 75}x^{3}$$

\frac{35\times 38}{408\times 75} kasridagi ko‘paytirishlarni bajaring.

$$\frac{1330}{30600}x^{3}$$

\frac{1330}{30600} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{133}{3060}x^{3}$$

x ga nisbatan hosilani topish

$$\frac{133x^{2}}{1020}$$

Derivativ ifodasidan foydalanish qadamlari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{6}x^{2}\times \frac{7}{10}\times \frac{5}{34}x\times \frac{38}{75})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{6}x^{3}\times \frac{7}{10}\times \frac{5}{34}\times \frac{38}{75})$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{6} ni \frac{7}{10} ga ko‘paytiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 7}{6\times 10}x^{3}\times \frac{5}{34}\times \frac{38}{75})$$

\frac{5\times 7}{6\times 10} kasridagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{35}{60}x^{3}\times \frac{5}{34}\times \frac{38}{75})$$

\frac{35}{60} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{12}x^{3}\times \frac{5}{34}\times \frac{38}{75})$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{7}{12} ni \frac{5}{34} ga ko‘paytiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7\times 5}{12\times 34}x^{3}\times \frac{38}{75})$$

\frac{7\times 5}{12\times 34} kasridagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{35}{408}x^{3}\times \frac{38}{75})$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{35}{408} ni \frac{38}{75} ga ko‘paytiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{35\times 38}{408\times 75}x^{3})$$

\frac{35\times 38}{408\times 75} kasridagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1330}{30600}x^{3})$$

\frac{1330}{30600} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{133}{3060}x^{3})$$

ax^{n} hosilasi – nax^{n-1}.

$$3\times \frac{133}{3060}x^{3-1}$$

3 ni \frac{133}{3060} marotabaga ko'paytirish.

$$\frac{133}{1020}x^{3-1}$$

3 dan 1 ni ayirish.

$$\frac{133}{1020}x^{2}$$