(sqrt{1/x-2})^2 eching

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

Baholash

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

Qisqa yechim qadamlari

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

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

\frac{1}{x} va \frac{2x}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

2 daraja ko‘rsatkichini \sqrt{\frac{1-2x}{x}} ga hisoblang va \frac{1-2x}{x} ni qiymatni oling.

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

x ga nisbatan hosilani topish

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

Koʻpaytma uchun derivativ qoidasidan foydalanish qadamlari

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

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

\frac{1}{x} va \frac{2x}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

2 daraja ko‘rsatkichini \sqrt{\frac{1-2x}{x}} ga hisoblang va \frac{1-2x}{x} ni qiymatni oling.

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

Har qanday ikki differensial funksiya uchun, ikki funksiya koʻpaytmasining hosilasi birinchi funksiya marotabasi, ikkinchi plyus hosilasi ikkinchi funksiya marotabasi birinchining hosilasidir.

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

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

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

Qisqartirish.

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

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

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

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

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

Qisqartirish.

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

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

\frac{1}{x} va \frac{2x}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

2 daraja ko‘rsatkichini \sqrt{\frac{1-2x}{x}} ga hisoblang va \frac{1-2x}{x} ni qiymatni oling.

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

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

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Keraksiz qavslarni olib tashlash.

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

O'xshash hadlarni birlashtirish.

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

-2 dan -2 ni ayirish.

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

Ikki yoki undan ko'p raqam koʻpaytmasini daraja ko'rsatkichiga oshirish uchun har bir raqamni daraja ko'rsatkichiga oshiring va ularning koʻpaytmasini chiqaring.

$$-\frac{x^{0}}{1^{2}x^{2}}$$

1 ni 2 daraja ko'rsatgichiga oshirish.

$$-\frac{x^{0}}{x^{2}}$$

1 ni 2 marotabaga ko'paytirish.

$$\frac{-x^{0}}{x^{2}}$$

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

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

Arifmetik hisobni amalga oshirish.

$$-x^{-2}$$