8x^2/32x^2+32x eching

$$\frac { 8 x ^ { 2 } } { 32 x ^ { 2 } + 32 x }$$

Baholash

$$\frac{x}{4\left(x+1\right)}$$

Qisqa yechim qadamlari

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{8x^{2}}{32x\left(x+1\right)}$$

Surat va maxrajdagi ikkala 8x ni qisqartiring.

$$\frac{x}{4\left(x+1\right)}$$

Ifodani kengaytiring.

$$\frac{x}{4x+4}$$

x ga nisbatan hosilani topish

$$\frac{1}{4\left(x+1\right)^{2}}$$

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.

$$\frac{\left(32x^{2}+32x^{1}\right)\frac{\mathrm{d}}{\mathrm{d}x}(8x^{2})-8x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(32x^{2}+32x^{1})}{\left(32x^{2}+32x^{1}\right)^{2}}$$

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

$$\frac{\left(32x^{2}+32x^{1}\right)\times 2\times 8x^{2-1}-8x^{2}\left(2\times 32x^{2-1}+32x^{1-1}\right)}{\left(32x^{2}+32x^{1}\right)^{2}}$$

Qisqartirish.

$$\frac{\left(32x^{2}+32x^{1}\right)\times 16x^{1}-8x^{2}\left(64x^{1}+32x^{0}\right)}{\left(32x^{2}+32x^{1}\right)^{2}}$$

32x^{2}+32x^{1} ni 16x^{1} marotabaga ko'paytirish.

$$\frac{32x^{2}\times 16x^{1}+32x^{1}\times 16x^{1}-8x^{2}\left(64x^{1}+32x^{0}\right)}{\left(32x^{2}+32x^{1}\right)^{2}}$$

8x^{2} ni 64x^{1}+32x^{0} marotabaga ko'paytirish.

$$\frac{32x^{2}\times 16x^{1}+32x^{1}\times 16x^{1}-\left(8x^{2}\times 64x^{1}+8x^{2}\times 32x^{0}\right)}{\left(32x^{2}+32x^{1}\right)^{2}}$$

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

$$\frac{32\times 16x^{2+1}+32\times 16x^{1+1}-\left(8\times 64x^{2+1}+8\times 32x^{2}\right)}{\left(32x^{2}+32x^{1}\right)^{2}}$$

Qisqartirish.

$$\frac{512x^{3}+512x^{2}-\left(512x^{3}+256x^{2}\right)}{\left(32x^{2}+32x^{1}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{256x^{2}}{\left(32x^{2}+32x^{1}\right)^{2}}$$

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

$$\frac{256x^{2}}{\left(32x^{2}+32x\right)^{2}}$$