f(x)=1/x+1+1 eching

$$f ( x ) = \frac { 1 } { x + 1 } + 1$$

Baholash

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

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.

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

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

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

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

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

x ga nisbatan hosilani topish

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

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.

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

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

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

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

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

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

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Keraksiz qavslarni olib tashlash.

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

O'xshash hadlarni birlashtirish.

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

1 dan 1 ni va 1 dan 2 ni ayiring.

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

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

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

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

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