4k^5*9k^4/3k^3= eching

$$\frac { 4 k ^ { 5 } \times 9 k ^ { 4 } } { 3 k ^ { 3 } } =$$

Baholash

$$12k^{6}$$

Yechim qadamlari

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

$$\frac{4k^{9}\times 9}{3k^{3}}$$

Surat va maxrajdagi ikkala 3k^{3} ni qisqartiring.

$$3\times 4k^{6}$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$12k^{6}$$

k ga nisbatan hosilani topish

$$72k^{5}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{36k^{4}}{3}k^{5-3})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}k}(12k^{4}k^{2})$$

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

$$2\times 12k^{4}k^{2-1}$$

Arifmetik hisobni amalga oshirish.

$$24k^{4}k^{1}$$

Har qanday t sharti uchun t^{1}=t.

$$24k^{4}k$$