2+1/1-frac{1{x+1}} eching

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

Baholash

$$3+\frac{1}{x}$$

Qisqa yechim qadamlari

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

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

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

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

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

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

1 ni \frac{x}{x+1} ga bo'lish 1 ga k'paytirish \frac{x}{x+1} ga qaytarish.

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

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

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

\frac{2x}{x} va \frac{x+1}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

2x+x+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{3x+1}{x}$$

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

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

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

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

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

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

1 ni \frac{x}{x+1} ga bo'lish 1 ga k'paytirish \frac{x}{x+1} ga qaytarish.

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

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

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

\frac{2x}{x} va \frac{x+1}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

2x+x+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x+1}{x})$$

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

$$\left(3x^{1}+1\right)\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x})+\frac{1}{x}\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1}+1)$$

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

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

Qisqartirish.

$$\left(3x^{1}+1\right)\left(-1\right)x^{-2}+\frac{1}{x}\times 3x^{0}$$

3x^{1}+1 ni -x^{-2} marotabaga ko'paytirish.

$$3x^{1}\left(-1\right)x^{-2}-x^{-2}+\frac{1}{x}\times 3x^{0}$$

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

$$-3x^{1-2}-x^{-2}+3\times \frac{1}{x}$$

Qisqartirish.

$$-3\times \frac{1}{x}-x^{-2}+3\times \frac{1}{x}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

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

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

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

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

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

1 ni \frac{x}{x+1} ga bo'lish 1 ga k'paytirish \frac{x}{x+1} ga qaytarish.

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

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

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

\frac{2x}{x} va \frac{x+1}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

2x+x+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x+1}{x})$$

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

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

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{x^{1}\times 3x^{0}-\left(3x^{1}+1\right)x^{0}}{\left(x^{1}\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\times 3x^{0}-\left(3x^{1}x^{0}+x^{0}\right)}{\left(x^{1}\right)^{2}}$$

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

$$\frac{3x^{1}-\left(3x^{1}+x^{0}\right)}{\left(x^{1}\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{3x^{1}-3x^{1}-x^{0}}{\left(x^{1}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(3-3\right)x^{1}-x^{0}}{\left(x^{1}\right)^{2}}$$

3 dan 3 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.

$$-x^{-2}$$