frac{(9)^{3}*27*t^4}{(3)^2*(3)^4*t^2} eching

$$\frac { ( 9 ) ^ { 3 } \times 27 \times t ^ { 4 } } { ( 3 ) ^ { 2 } \times ( 3 ) ^ { 4 } \times t ^ { 2 } }$$

Baholash

$$27t^{2}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 4 ni qo‘shib, 6 ni oling.

$$\frac{9^{3}\times 27t^{4}}{3^{6}t^{2}}$$

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

$$\frac{27\times 9^{3}t^{2}}{3^{6}}$$

3 daraja ko‘rsatkichini 9 ga hisoblang va 729 ni qiymatni oling.

$$\frac{27\times 729t^{2}}{3^{6}}$$

19683 hosil qilish uchun 27 va 729 ni ko'paytirish.

$$\frac{19683t^{2}}{3^{6}}$$

6 daraja ko‘rsatkichini 3 ga hisoblang va 729 ni qiymatni oling.

$$\frac{19683t^{2}}{729}$$

27t^{2} ni olish uchun 19683t^{2} ni 729 ga bo‘ling.

$$27t^{2}$$

t ga nisbatan hosilani topish

$$54t$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{19683}{729}t^{4-2})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}t}(27t^{2})$$

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

$$2\times 27t^{2-1}$$

Arifmetik hisobni amalga oshirish.

$$54t^{1}$$

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

$$54t$$