a^5+5/6a^3*3/5a^2= eching

$$a ^ { 5 } + \frac { 5 } { 6 } a ^ { 3 } \cdot \frac { 3 } { 5 } a ^ { 2 } =$$

Baholash

$$\frac{3a^{5}}{2}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 2 ni qo‘shib, 5 ni oling.

$$a^{5}+\frac{5}{6}a^{5}\times \frac{3}{5}$$

\frac{1}{2} hosil qilish uchun \frac{5}{6} va \frac{3}{5} ni ko'paytirish.

$$a^{5}+\frac{1}{2}a^{5}$$

\frac{3}{2}a^{5} ni olish uchun a^{5} va \frac{1}{2}a^{5} ni birlashtirish.

$$\frac{3}{2}a^{5}$$

a ga nisbatan hosilani topish

$$\frac{15a^{4}}{2}$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

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

$$5a^{5-1}+3\times \frac{\frac{5}{2}a^{2}}{5}a^{3-1}$$

5 dan 1 ni ayirish.

$$5a^{4}+3\times \frac{\frac{5}{2}a^{2}}{5}a^{3-1}$$

3 ni \frac{3}{5}\times \frac{5}{6}a^{2} marotabaga ko'paytirish.

$$5a^{4}+\frac{3a^{2}}{2}a^{3-1}$$

3 dan 1 ni ayirish.

$$5a^{4}+\frac{3a^{2}}{2}a^{2}$$