x/x-frac{1{x}} eching

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

Baholash

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

Qisqa yechim qadamlari

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

$$\frac{x}{\frac{xx}{x}-\frac{1}{x}}$$

\frac{xx}{x} va \frac{1}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x}{\frac{xx-1}{x}}$$

xx-1 ichidagi ko‘paytirishlarni bajaring.

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

x ni \frac{x^{2}-1}{x} ga bo'lish x ga k'paytirish \frac{x^{2}-1}{x} ga qaytarish.

$$\frac{xx}{x^{2}-1}$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

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

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

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

Qisqartirish.

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

x^{1}-\frac{1}{x} ni x^{0} marotabaga ko'paytirish.

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

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

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

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

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

Qisqartirish.

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

O'xshash hadlarni birlashtirish.

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

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

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