a+b-a/1+ab/1-frac{ab-a^2{1+ab}} eching

$$\frac { a + \frac { b - a } { 1 + a b } } { 1 - \frac { a b - a ^ { 2 } } { 1 + a b } }$$

Baholash

$$b$$

Qisqa yechim qadamlari

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

$$\frac{\frac{a\left(1+ab\right)}{1+ab}+\frac{b-a}{1+ab}}{1-\frac{ab-a^{2}}{1+ab}}$$

\frac{a\left(1+ab\right)}{1+ab} va \frac{b-a}{1+ab} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{a\left(1+ab\right)+b-a}{1+ab}}{1-\frac{ab-a^{2}}{1+ab}}$$

a\left(1+ab\right)+b-a ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{a+a^{2}b+b-a}{1+ab}}{1-\frac{ab-a^{2}}{1+ab}}$$

a+a^{2}b+b-a kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{b+a^{2}b}{1+ab}}{1-\frac{ab-a^{2}}{1+ab}}$$

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

$$\frac{\frac{b+a^{2}b}{1+ab}}{\frac{1+ab}{1+ab}-\frac{ab-a^{2}}{1+ab}}$$

\frac{1+ab}{1+ab} va \frac{ab-a^{2}}{1+ab} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{b+a^{2}b}{1+ab}}{\frac{1+ab-\left(ab-a^{2}\right)}{1+ab}}$$

1+ab-\left(ab-a^{2}\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{b+a^{2}b}{1+ab}}{\frac{1+ab-ab+a^{2}}{1+ab}}$$

1+ab-ab+a^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{b+a^{2}b}{1+ab}}{\frac{1+a^{2}}{1+ab}}$$

\frac{b+a^{2}b}{1+ab} ni \frac{1+a^{2}}{1+ab} ga bo'lish \frac{b+a^{2}b}{1+ab} ga k'paytirish \frac{1+a^{2}}{1+ab} ga qaytarish.

$$\frac{\left(b+a^{2}b\right)\left(1+ab\right)}{\left(1+ab\right)\left(1+a^{2}\right)}$$

Surat va maxrajdagi ikkala ab+1 ni qisqartiring.

$$\frac{ba^{2}+b}{a^{2}+1}$$

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{b\left(a^{2}+1\right)}{a^{2}+1}$$

Surat va maxrajdagi ikkala a^{2}+1 ni qisqartiring.

$$b$$

b ga nisbatan hosilani topish

$$1$$

Derivativ ifodasidan foydalanish qadamlari

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

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

\frac{a\left(1+ab\right)}{1+ab} va \frac{b-a}{1+ab} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

a\left(1+ab\right)+b-a ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\frac{a+a^{2}b+b-a}{1+ab}}{1-\frac{ab-a^{2}}{1+ab}})$$

a+a^{2}b+b-a kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\frac{b+a^{2}b}{1+ab}}{1-\frac{ab-a^{2}}{1+ab}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\frac{b+a^{2}b}{1+ab}}{\frac{1+ab}{1+ab}-\frac{ab-a^{2}}{1+ab}})$$

\frac{1+ab}{1+ab} va \frac{ab-a^{2}}{1+ab} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

1+ab-\left(ab-a^{2}\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\frac{b+a^{2}b}{1+ab}}{\frac{1+ab-ab+a^{2}}{1+ab}})$$

1+ab-ab+a^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\frac{b+a^{2}b}{1+ab}}{\frac{1+a^{2}}{1+ab}})$$

\frac{b+a^{2}b}{1+ab} ni \frac{1+a^{2}}{1+ab} ga bo'lish \frac{b+a^{2}b}{1+ab} ga k'paytirish \frac{1+a^{2}}{1+ab} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\left(b+a^{2}b\right)\left(1+ab\right)}{\left(1+ab\right)\left(1+a^{2}\right)})$$

Surat va maxrajdagi ikkala ab+1 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{ba^{2}+b}{a^{2}+1})$$

\frac{ba^{2}+b}{a^{2}+1} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b\left(a^{2}+1\right)}{a^{2}+1})$$

Surat va maxrajdagi ikkala a^{2}+1 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b)$$

ax^{n} hosilasi – nax^{n-1}.

$$b^{1-1}$$

1 dan 1 ni ayirish.

$$b^{0}$$

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

$$1$$