25*t^-4/5^-3*10*t^-8 eching

$$\frac { 25 \times t ^ { - 4 } } { 5 ^ { - 3 } \times 10 \times t ^ { - 8 } }$$

Baholash

$$\frac{625t^{4}}{2}$$

Yechim qadamlari

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\frac{5t^{-4}}{2\times 5^{-3}t^{-8}}$$

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

$$\frac{5^{4}t^{4}}{2}$$

4 daraja ko‘rsatkichini 5 ga hisoblang va 625 ni qiymatni oling.

$$\frac{625t^{4}}{2}$$

t ga nisbatan hosilani topish

$$1250t^{3}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{25}{\frac{2}{25}}t^{-4-\left(-8\right)})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{625}{2}t^{4})$$

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

$$4\times \frac{625}{2}t^{4-1}$$

Arifmetik hisobni amalga oshirish.

$$1250t^{3}$$