1/x-1/x+1= eching

$$\frac { 1 } { x } - \frac { 1 } { x + 1 } =$$

Baholash

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

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{1}{x} ni \frac{x+1}{x+1} marotabaga ko'paytirish. \frac{1}{x+1} ni \frac{x}{x} marotabaga ko'paytirish.

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

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

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

x+1-x kabi iboralarga o‘xshab birlashtiring.

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

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

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

x ga nisbatan hosilani topish

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

Zanjirli qoidadan foydalanish qadamalari

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{1}{x} ni \frac{x+1}{x+1} marotabaga ko'paytirish. \frac{1}{x+1} ni \frac{x}{x} marotabaga ko'paytirish.

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

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

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

x+1-x kabi iboralarga o‘xshab birlashtiring.

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

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

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

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.

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

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

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

Qisqartirish.

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

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

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

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

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