x/7*14/x+9 eching

$$\frac { x } { 7 } \cdot \frac { 14 } { x + 9 }$$

Baholash

$$\frac{2x}{x+9}$$

Yechim qadamlari

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x}{7} ni \frac{14}{x+9} ga ko‘paytiring.

$$\frac{x\times 14}{7\left(x+9\right)}$$

Surat va maxrajdagi ikkala 7 ni qisqartiring.

$$\frac{2x}{x+9}$$

x ga nisbatan hosilani topish

$$\frac{18}{\left(x+9\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x}{7} ni \frac{14}{x+9} ga ko‘paytiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times 14}{7\left(x+9\right)})$$

Surat va maxrajdagi ikkala 7 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x}{x+9})$$

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

$$\frac{\left(x^{1}+9\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1})-2x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+9)}{\left(x^{1}+9\right)^{2}}$$

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

$$\frac{\left(x^{1}+9\right)\times 2x^{1-1}-2x^{1}x^{1-1}}{\left(x^{1}+9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{1}+9\right)\times 2x^{0}-2x^{1}x^{0}}{\left(x^{1}+9\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\times 2x^{0}+9\times 2x^{0}-2x^{1}x^{0}}{\left(x^{1}+9\right)^{2}}$$

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

$$\frac{2x^{1}+9\times 2x^{0}-2x^{1}}{\left(x^{1}+9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{2x^{1}+18x^{0}-2x^{1}}{\left(x^{1}+9\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(2-2\right)x^{1}+18x^{0}}{\left(x^{1}+9\right)^{2}}$$

2 dan 2 ni ayirish.

$$\frac{18x^{0}}{\left(x^{1}+9\right)^{2}}$$

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

$$\frac{18x^{0}}{\left(x+9\right)^{2}}$$

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

$$\frac{18\times 1}{\left(x+9\right)^{2}}$$

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

$$\frac{18}{\left(x+9\right)^{2}}$$