5(2x/x+3) eching

$$5 ( \frac { 2 x } { x + 3 } )$$

Baholash

$$\frac{10x}{x+3}$$

Yechim qadamlari

5\times \frac{2x}{x+3} ni yagona kasrga aylantiring.

$$\frac{5\times 2x}{x+3}$$

10 hosil qilish uchun 5 va 2 ni ko'paytirish.

$$\frac{10x}{x+3}$$

x ga nisbatan hosilani topish

$$\frac{30}{\left(x+3\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

5\times \frac{2x}{x+3} ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 2x}{x+3})$$

10 hosil qilish uchun 5 va 2 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10x}{x+3})$$

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

$$\frac{\left(x^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}x}(10x^{1})-10x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+3)}{\left(x^{1}+3\right)^{2}}$$

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

$$\frac{\left(x^{1}+3\right)\times 10x^{1-1}-10x^{1}x^{1-1}}{\left(x^{1}+3\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{1}+3\right)\times 10x^{0}-10x^{1}x^{0}}{\left(x^{1}+3\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\times 10x^{0}+3\times 10x^{0}-10x^{1}x^{0}}{\left(x^{1}+3\right)^{2}}$$

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

$$\frac{10x^{1}+3\times 10x^{0}-10x^{1}}{\left(x^{1}+3\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{10x^{1}+30x^{0}-10x^{1}}{\left(x^{1}+3\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(10-10\right)x^{1}+30x^{0}}{\left(x^{1}+3\right)^{2}}$$

10 dan 10 ni ayirish.

$$\frac{30x^{0}}{\left(x^{1}+3\right)^{2}}$$

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

$$\frac{30x^{0}}{\left(x+3\right)^{2}}$$

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

$$\frac{30\times 1}{\left(x+3\right)^{2}}$$

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

$$\frac{30}{\left(x+3\right)^{2}}$$