1/x+6-1/x+7 eching

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

Baholash

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

Qisqa yechim qadamlari

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

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

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

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

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

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

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

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

\left(x+6\right)\left(x+7\right) ni kengaytirish.

$$\frac{1}{x^{2}+13x+42}$$

x ga nisbatan hosilani topish

$$\frac{-2x-13}{\left(\left(x+6\right)\left(x+7\right)\right)^{2}}$$

Zanjirli qoidadan foydalanish qadamalari

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

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

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

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

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

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

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

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

x+6 ifodaning har bir elementini x+7 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{2}+7x+6x+42})$$

13x ni olish uchun 7x va 6x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{2}+13x+42})$$

Agar F ikki differensial funksiya f\left(u\right) va u=g\left(x\right)'ning yig'indisi bo'lsa, ya'ni agar F\left(x\right)=f\left(g\left(x\right)\right) bo'lsa, F hosilasi f'ning u martalik hosilasi, g'ning x martalik hosilasi ya'ni \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right) bo'ladi.

$$-\left(x^{2}+13x^{1}+42\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+13x^{1}+42)$$

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

$$-\left(x^{2}+13x^{1}+42\right)^{-2}\left(2x^{2-1}+13x^{1-1}\right)$$

Qisqartirish.

$$\left(x^{2}+13x^{1}+42\right)^{-2}\left(-2x^{1}-13x^{0}\right)$$

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

$$\left(x^{2}+13x+42\right)^{-2}\left(-2x-13x^{0}\right)$$

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

$$\left(x^{2}+13x+42\right)^{-2}\left(-2x-13\right)$$