5/frac{7{x}+2} eching

$$\frac { 5 } { \frac { 7 } { x } + 2 }$$

Baholash

$$\frac{5x}{2x+7}$$

Yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{5}{\frac{7}{x}+\frac{2x}{x}}$$

\frac{7}{x} va \frac{2x}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{5}{\frac{7+2x}{x}}$$

5 ni \frac{7+2x}{x} ga bo'lish 5 ga k'paytirish \frac{7+2x}{x} ga qaytarish.

$$\frac{5x}{7+2x}$$

x ga nisbatan hosilani topish

$$\frac{35}{\left(2x+7\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{\frac{7}{x}+\frac{2x}{x}})$$

\frac{7}{x} va \frac{2x}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{\frac{7+2x}{x}})$$

5 ni \frac{7+2x}{x} ga bo'lish 5 ga k'paytirish \frac{7+2x}{x} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{7+2x})$$

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

$$\frac{\left(2x^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1})-5x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}+7)}{\left(2x^{1}+7\right)^{2}}$$

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

$$\frac{\left(2x^{1}+7\right)\times 5x^{1-1}-5x^{1}\times 2x^{1-1}}{\left(2x^{1}+7\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(2x^{1}+7\right)\times 5x^{0}-5x^{1}\times 2x^{0}}{\left(2x^{1}+7\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{2x^{1}\times 5x^{0}+7\times 5x^{0}-5x^{1}\times 2x^{0}}{\left(2x^{1}+7\right)^{2}}$$

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

$$\frac{2\times 5x^{1}+7\times 5x^{0}-5\times 2x^{1}}{\left(2x^{1}+7\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{10x^{1}+35x^{0}-10x^{1}}{\left(2x^{1}+7\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(10-10\right)x^{1}+35x^{0}}{\left(2x^{1}+7\right)^{2}}$$

10 dan 10 ni ayirish.

$$\frac{35x^{0}}{\left(2x^{1}+7\right)^{2}}$$

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

$$\frac{35x^{0}}{\left(2x+7\right)^{2}}$$

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

$$\frac{35\times 1}{\left(2x+7\right)^{2}}$$

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

$$\frac{35}{\left(2x+7\right)^{2}}$$