frac{2x^{2}y^2}{4x^2+7^4*3x^-3} eching

$$\frac { 2 x ^ { 2 } y ^ { 2 } } { 4 x ^ { 2 } + 7 ^ { 4 } \cdot 3 x ^ { - 3 } }$$

Baholash

$$\frac{2y^{2}x^{5}}{4x^{5}+7203}$$

Qisqa yechim qadamlari

4 daraja ko‘rsatkichini 7 ga hisoblang va 2401 ni qiymatni oling.

$$\frac{2x^{2}y^{2}}{4x^{2}+2401\times 3x^{-3}}$$

7203 hosil qilish uchun 2401 va 3 ni ko'paytirish.

$$\frac{2x^{2}y^{2}}{4x^{2}+7203x^{-3}}$$

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{2x^{2}y^{2}}{x^{-3}\left(4x^{5}+7203\right)}$$

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

$$\frac{2y^{2}x^{5}}{4x^{5}+7203}$$

x ga nisbatan hosilani topish

$$72030\times \left(\frac{y}{4x^{5}+7203}\right)^{2}x^{4}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Har qanday ikki differensial funksiya uchun ikki funksiyaning koeffitsient hosilasi raqamlagichning hosila marotabasi maxraj minusi va barchasi kvadrat maxrajiga bo'lingan.

$$\frac{\left(4x^{2}+7203x^{-3}\right)\frac{\mathrm{d}}{\mathrm{d}x}(2y^{2}x^{2})-2y^{2}x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2}+7203x^{-3})}{\left(4x^{2}+7203x^{-3}\right)^{2}}$$

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

$$\frac{\left(4x^{2}+7203x^{-3}\right)\times 2\times 2y^{2}x^{2-1}-2y^{2}x^{2}\left(2\times 4x^{2-1}-3\times 7203x^{-3-1}\right)}{\left(4x^{2}+7203x^{-3}\right)^{2}}$$

Qisqartirish.

$$\frac{\left(4x^{2}+7203x^{-3}\right)\times 4y^{2}x^{1}-2y^{2}x^{2}\left(8x^{1}-21609x^{-4}\right)}{\left(4x^{2}+7203x^{-3}\right)^{2}}$$

4x^{2}+7203x^{-3} ni 4y^{2}x^{1} marotabaga ko'paytirish.

$$\frac{4x^{2}\times 4y^{2}x^{1}+7203x^{-3}\times 4y^{2}x^{1}-2y^{2}x^{2}\left(8x^{1}-21609x^{-4}\right)}{\left(4x^{2}+7203x^{-3}\right)^{2}}$$

2y^{2}x^{2} ni 8x^{1}-21609x^{-4} marotabaga ko'paytirish.

$$\frac{4x^{2}\times 4y^{2}x^{1}+7203x^{-3}\times 4y^{2}x^{1}-\left(2y^{2}x^{2}\times 8x^{1}+2y^{2}x^{2}\left(-21609\right)x^{-4}\right)}{\left(4x^{2}+7203x^{-3}\right)^{2}}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$\frac{4\times 4y^{2}x^{2+1}+7203\times 4y^{2}x^{-3+1}-\left(2y^{2}\times 8x^{2+1}+2y^{2}\left(-21609\right)x^{2-4}\right)}{\left(4x^{2}+7203x^{-3}\right)^{2}}$$

Qisqartirish.

$$\frac{16y^{2}x^{3}+28812y^{2}x^{-2}-\left(16y^{2}x^{3}+\left(-43218y^{2}\right)x^{-2}\right)}{\left(4x^{2}+7203x^{-3}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{72030y^{2}x^{-2}}{\left(4x^{2}+7203x^{-3}\right)^{2}}$$