3/2x*(x^2/6x+10) eching

$$\frac{ 3 }{ 2x } \times ( \frac{ { x }^{ 2 } }{ 6x+10 } )$$

Baholash

$$\frac{3x}{4\left(3x+5\right)}$$

Qisqa yechim qadamlari

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{2x} ni \frac{x^{2}}{6x+10} ga ko‘paytiring.

$$\frac{3x^{2}}{2x\left(6x+10\right)}$$

Surat va maxrajdagi ikkala x ni qisqartiring.

$$\frac{3x}{2\left(6x+10\right)}$$

2 ga 6x+10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3x}{12x+20}$$

x ga nisbatan hosilani topish

$$\frac{15}{4\left(3x+5\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{2x} ni \frac{x^{2}}{6x+10} ga ko‘paytiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x^{2}}{2x\left(6x+10\right)})$$

Surat va maxrajdagi ikkala x ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x}{2\left(6x+10\right)})$$

2 ga 6x+10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x}{12x+20})$$

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

$$\frac{\left(12x^{1}+20\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1})-3x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(12x^{1}+20)}{\left(12x^{1}+20\right)^{2}}$$

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

$$\frac{\left(12x^{1}+20\right)\times 3x^{1-1}-3x^{1}\times 12x^{1-1}}{\left(12x^{1}+20\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(12x^{1}+20\right)\times 3x^{0}-3x^{1}\times 12x^{0}}{\left(12x^{1}+20\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{12x^{1}\times 3x^{0}+20\times 3x^{0}-3x^{1}\times 12x^{0}}{\left(12x^{1}+20\right)^{2}}$$

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

$$\frac{12\times 3x^{1}+20\times 3x^{0}-3\times 12x^{1}}{\left(12x^{1}+20\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{36x^{1}+60x^{0}-36x^{1}}{\left(12x^{1}+20\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(36-36\right)x^{1}+60x^{0}}{\left(12x^{1}+20\right)^{2}}$$

36 dan 36 ni ayirish.

$$\frac{60x^{0}}{\left(12x^{1}+20\right)^{2}}$$

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

$$\frac{60x^{0}}{\left(12x+20\right)^{2}}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$\frac{60\times 1}{\left(12x+20\right)^{2}}$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{60}{\left(12x+20\right)^{2}}$$