5/x-1-4/4x eching

$$\frac { 5 } { x - 1 } - \frac { 4 } { 4 x }$$

Baholash

$$\frac{4x+1}{x\left(x-1\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-1 va 4x ning eng kichik umumiy karralisi 4x\left(x-1\right). \frac{5}{x-1} ni \frac{4x}{4x} marotabaga ko'paytirish. \frac{4}{4x} ni \frac{x-1}{x-1} marotabaga ko'paytirish.

$$\frac{5\times 4x}{4x\left(x-1\right)}-\frac{4\left(x-1\right)}{4x\left(x-1\right)}$$

\frac{5\times 4x}{4x\left(x-1\right)} va \frac{4\left(x-1\right)}{4x\left(x-1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{5\times 4x-4\left(x-1\right)}{4x\left(x-1\right)}$$

5\times 4x-4\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{20x-4x+4}{4x\left(x-1\right)}$$

20x-4x+4 kabi iboralarga o‘xshab birlashtiring.

$$\frac{16x+4}{4x\left(x-1\right)}$$

\frac{16x+4}{4x\left(x-1\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{4\left(4x+1\right)}{4x\left(x-1\right)}$$

Surat va maxrajdagi ikkala 4 ni qisqartiring.

$$\frac{4x+1}{x\left(x-1\right)}$$

x\left(x-1\right) ni kengaytirish.

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

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-1 va 4x ning eng kichik umumiy karralisi 4x\left(x-1\right). \frac{5}{x-1} ni \frac{4x}{4x} marotabaga ko'paytirish. \frac{4}{4x} ni \frac{x-1}{x-1} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 4x}{4x\left(x-1\right)}-\frac{4\left(x-1\right)}{4x\left(x-1\right)})$$

\frac{5\times 4x}{4x\left(x-1\right)} va \frac{4\left(x-1\right)}{4x\left(x-1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 4x-4\left(x-1\right)}{4x\left(x-1\right)})$$

5\times 4x-4\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20x-4x+4}{4x\left(x-1\right)})$$

20x-4x+4 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16x+4}{4x\left(x-1\right)})$$

\frac{16x+4}{4x\left(x-1\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(4x+1\right)}{4x\left(x-1\right)})$$

Surat va maxrajdagi ikkala 4 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x+1}{x\left(x-1\right)})$$

x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x+1}{x^{2}-x})$$

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

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

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

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

Qisqartirish.

$$\frac{\left(x^{2}-x^{1}\right)\times 4x^{0}-\left(4x^{1}+1\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}\right)^{2}}$$

x^{2}-x^{1} ni 4x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 4x^{0}-x^{1}\times 4x^{0}-\left(4x^{1}+1\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}\right)^{2}}$$

4x^{1}+1 ni 2x^{1}-x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 4x^{0}-x^{1}\times 4x^{0}-\left(4x^{1}\times 2x^{1}+4x^{1}\left(-1\right)x^{0}+2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}\right)^{2}}$$

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

$$\frac{4x^{2}-4x^{1}-\left(4\times 2x^{1+1}+4\left(-1\right)x^{1}+2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}\right)^{2}}$$

Qisqartirish.

$$\frac{4x^{2}-4x^{1}-\left(8x^{2}-4x^{1}+2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-4x^{2}-2x^{1}+x^{0}}{\left(x^{2}-x^{1}\right)^{2}}$$

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

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

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

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