(5^5*p^7)div(25*p^3) eching

$$( 5 ^ { 5 } \times p ^ { 7 } ) \div ( 25 \times p ^ { 3 } )$$

Baholash

$$125p^{4}$$

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{5^{5}p^{7}}{25^{1}p^{3}}$$

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

$$\frac{5^{5}p^{7-3}}{25^{1}}$$

7 dan 3 ni ayirish.

$$\frac{5^{5}p^{4}}{25^{1}}$$

5 ni 5 daraja ko'rsatgichiga oshirish.

$$\frac{3125p^{4}}{25^{1}}$$

3125 ni 25 ga bo'lish.

$$125p^{4}$$

p ga nisbatan hosilani topish

$$500p^{3}$$

Derivativ ifodasidan foydalanish qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{5^{5}p^{4}}{25})$$

5 daraja ko‘rsatkichini 5 ga hisoblang va 3125 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{3125p^{4}}{25})$$

125p^{4} ni olish uchun 3125p^{4} ni 25 ga bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}p}(125p^{4})$$

ax^{n} hosilasi – nax^{n-1}.

$$4\times 125p^{4-1}$$

4 ni 125 marotabaga ko'paytirish.

$$500p^{4-1}$$

4 dan 1 ni ayirish.

$$500p^{3}$$