7/x-6/x+1 eching

$$\frac { 7 } { x } - \frac { 6 } { x + 1 }$$

Baholash

$$\frac{x+7}{x\left(x+1\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x va x+1 ning eng kichik umumiy karralisi x\left(x+1\right). \frac{7}{x} ni \frac{x+1}{x+1} marotabaga ko'paytirish. \frac{6}{x+1} ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{7\left(x+1\right)}{x\left(x+1\right)}-\frac{6x}{x\left(x+1\right)}$$

\frac{7\left(x+1\right)}{x\left(x+1\right)} va \frac{6x}{x\left(x+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{7\left(x+1\right)-6x}{x\left(x+1\right)}$$

7\left(x+1\right)-6x ichidagi ko‘paytirishlarni bajaring.

$$\frac{7x+7-6x}{x\left(x+1\right)}$$

7x+7-6x kabi iboralarga o‘xshab birlashtiring.

$$\frac{x+7}{x\left(x+1\right)}$$

x\left(x+1\right) ni kengaytirish.

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

x ga nisbatan hosilani topish

$$-\frac{x^{2}+14x+7}{\left(x\left(x+1\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x va x+1 ning eng kichik umumiy karralisi x\left(x+1\right). \frac{7}{x} ni \frac{x+1}{x+1} marotabaga ko'paytirish. \frac{6}{x+1} ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7\left(x+1\right)}{x\left(x+1\right)}-\frac{6x}{x\left(x+1\right)})$$

\frac{7\left(x+1\right)}{x\left(x+1\right)} va \frac{6x}{x\left(x+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7\left(x+1\right)-6x}{x\left(x+1\right)})$$

7\left(x+1\right)-6x ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x+7-6x}{x\left(x+1\right)})$$

7x+7-6x kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+7}{x\left(x+1\right)})$$

x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

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

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

Qisqartirish.

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

x^{2}+x^{1} ni x^{0} marotabaga ko'paytirish.

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

x^{1}+7 ni 2x^{1}+x^{0} marotabaga ko'paytirish.

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

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

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

Qisqartirish.

$$\frac{x^{2}+x^{1}-\left(2x^{2}+x^{1}+14x^{1}+7x^{0}\right)}{\left(x^{2}+x^{1}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-x^{2}-14x^{1}-7x^{0}}{\left(x^{2}+x^{1}\right)^{2}}$$

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

$$\frac{-x^{2}-14x-7x^{0}}{\left(x^{2}+x\right)^{2}}$$

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

$$\frac{-x^{2}-14x-7}{\left(x^{2}+x\right)^{2}}$$