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

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

Baholash

$$\frac{x}{6x+25}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 ni \frac{x+5}{x+5} marotabaga ko'paytirish.

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

\frac{x}{x+5} va \frac{5\left(x+5\right)}{x+5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

x+5\left(x+5\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{x}{x+5}}{\frac{x+5x+25}{x+5}}$$

x+5x+25 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{x}{x+5}}{\frac{6x+25}{x+5}}$$

\frac{x}{x+5} ni \frac{6x+25}{x+5} ga bo'lish \frac{x}{x+5} ga k'paytirish \frac{6x+25}{x+5} ga qaytarish.

$$\frac{x\left(x+5\right)}{\left(x+5\right)\left(6x+25\right)}$$

Surat va maxrajdagi ikkala x+5 ni qisqartiring.

$$\frac{x}{6x+25}$$

x ga nisbatan hosilani topish

$$\frac{25}{\left(6x+25\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 ni \frac{x+5}{x+5} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{x+5}}{\frac{x}{x+5}+\frac{5\left(x+5\right)}{x+5}})$$

\frac{x}{x+5} va \frac{5\left(x+5\right)}{x+5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{x+5}}{\frac{x+5\left(x+5\right)}{x+5}})$$

x+5\left(x+5\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{x+5}}{\frac{x+5x+25}{x+5}})$$

x+5x+25 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{x+5}}{\frac{6x+25}{x+5}})$$

\frac{x}{x+5} ni \frac{6x+25}{x+5} ga bo'lish \frac{x}{x+5} ga k'paytirish \frac{6x+25}{x+5} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(x+5\right)}{\left(x+5\right)\left(6x+25\right)})$$

Surat va maxrajdagi ikkala x+5 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{6x+25})$$

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

$$\frac{\left(6x^{1}+25\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})-x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(6x^{1}+25)}{\left(6x^{1}+25\right)^{2}}$$

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

$$\frac{\left(6x^{1}+25\right)x^{1-1}-x^{1}\times 6x^{1-1}}{\left(6x^{1}+25\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(6x^{1}+25\right)x^{0}-x^{1}\times 6x^{0}}{\left(6x^{1}+25\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{6x^{1}x^{0}+25x^{0}-x^{1}\times 6x^{0}}{\left(6x^{1}+25\right)^{2}}$$

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

$$\frac{6x^{1}+25x^{0}-6x^{1}}{\left(6x^{1}+25\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(6-6\right)x^{1}+25x^{0}}{\left(6x^{1}+25\right)^{2}}$$

6 dan 6 ni ayirish.

$$\frac{25x^{0}}{\left(6x^{1}+25\right)^{2}}$$

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

$$\frac{25x^{0}}{\left(6x+25\right)^{2}}$$

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

$$\frac{25\times 1}{\left(6x+25\right)^{2}}$$

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

$$\frac{25}{\left(6x+25\right)^{2}}$$