x/frac{4{x^2}-1}= eching

$$\frac { x } { \frac { 4 } { x ^ { 2 } } - 1 } =$$

Baholash

$$-\frac{x^{3}}{x^{2}-4}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{x^{2}}{x^{2}} marotabaga ko'paytirish.

$$\frac{x}{\frac{4}{x^{2}}-\frac{x^{2}}{x^{2}}}$$

\frac{4}{x^{2}} va \frac{x^{2}}{x^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x}{\frac{4-x^{2}}{x^{2}}}$$

x ni \frac{4-x^{2}}{x^{2}} ga bo'lish x ga k'paytirish \frac{4-x^{2}}{x^{2}} ga qaytarish.

$$\frac{xx^{2}}{4-x^{2}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

$$\frac{x^{3}}{4-x^{2}}$$

x ga nisbatan hosilani topish

$$\left(\frac{x}{x^{2}-4}\right)^{2}\left(12-x^{2}\right)$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{x^{2}}{x^{2}} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\frac{4}{x^{2}}-\frac{x^{2}}{x^{2}}})$$

\frac{4}{x^{2}} va \frac{x^{2}}{x^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\frac{4-x^{2}}{x^{2}}})$$

x ni \frac{4-x^{2}}{x^{2}} ga bo'lish x ga k'paytirish \frac{4-x^{2}}{x^{2}} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx^{2}}{4-x^{2}})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}}{4-x^{2}})$$

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

$$\frac{\left(-x^{2}+4\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{3})-x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+4)}{\left(-x^{2}+4\right)^{2}}$$

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

$$\frac{\left(-x^{2}+4\right)\times 3x^{3-1}-x^{3}\times 2\left(-1\right)x^{2-1}}{\left(-x^{2}+4\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(-x^{2}+4\right)\times 3x^{2}-x^{3}\left(-2\right)x^{1}}{\left(-x^{2}+4\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{-x^{2}\times 3x^{2}+4\times 3x^{2}-x^{3}\left(-2\right)x^{1}}{\left(-x^{2}+4\right)^{2}}$$

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

$$\frac{-3x^{2+2}+4\times 3x^{2}-\left(-2x^{3+1}\right)}{\left(-x^{2}+4\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{-3x^{4}+12x^{2}-\left(-2x^{4}\right)}{\left(-x^{2}+4\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-3-\left(-2\right)\right)x^{4}+12x^{2}}{\left(-x^{2}+4\right)^{2}}$$

-3 dan -2 ni ayirish.

$$\frac{-x^{4}+12x^{2}}{\left(-x^{2}+4\right)^{2}}$$

x^{2} omili.

$$\frac{x^{2}\left(-x^{2}+12x^{0}\right)}{\left(-x^{2}+4\right)^{2}}$$

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

$$\frac{x^{2}\left(-x^{2}+12\times 1\right)}{\left(-x^{2}+4\right)^{2}}$$

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

$$\frac{x^{2}\left(-x^{2}+12\right)}{\left(-x^{2}+4\right)^{2}}$$