f(x)=4x+1/4x-5 eching

$$f ( x ) = 4 x + \frac { 1 } { 4 x - 5 }$$

Baholash

$$\frac{16x^{2}-20x+1}{4x-5}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4x ni \frac{4x-5}{4x-5} marotabaga ko'paytirish.

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

\frac{4x\left(4x-5\right)}{4x-5} va \frac{1}{4x-5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

$$\frac{16x^{2}-20x+1}{4x-5}$$

x ga nisbatan hosilani topish

$$\frac{32\left(x-1\right)\left(2x-3\right)}{\left(4x-5\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4x ni \frac{4x-5}{4x-5} marotabaga ko'paytirish.

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

\frac{4x\left(4x-5\right)}{4x-5} va \frac{1}{4x-5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16x^{2}-20x+1}{4x-5})$$

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

$$\frac{\left(4x^{1}-5\right)\frac{\mathrm{d}}{\mathrm{d}x}(16x^{2}-20x^{1}+1)-\left(16x^{2}-20x^{1}+1\right)\frac{\mathrm{d}}{\mathrm{d}x}(4x^{1}-5)}{\left(4x^{1}-5\right)^{2}}$$

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

$$\frac{\left(4x^{1}-5\right)\left(2\times 16x^{2-1}-20x^{1-1}\right)-\left(16x^{2}-20x^{1}+1\right)\times 4x^{1-1}}{\left(4x^{1}-5\right)^{2}}$$

Qisqartirish.

$$\frac{\left(4x^{1}-5\right)\left(32x^{1}-20x^{0}\right)-\left(16x^{2}-20x^{1}+1\right)\times 4x^{0}}{\left(4x^{1}-5\right)^{2}}$$

4x^{1}-5 ni 32x^{1}-20x^{0} marotabaga ko'paytirish.

$$\frac{4x^{1}\times 32x^{1}+4x^{1}\left(-20\right)x^{0}-5\times 32x^{1}-5\left(-20\right)x^{0}-\left(16x^{2}-20x^{1}+1\right)\times 4x^{0}}{\left(4x^{1}-5\right)^{2}}$$

16x^{2}-20x^{1}+1 ni 4x^{0} marotabaga ko'paytirish.

$$\frac{4x^{1}\times 32x^{1}+4x^{1}\left(-20\right)x^{0}-5\times 32x^{1}-5\left(-20\right)x^{0}-\left(16x^{2}\times 4x^{0}-20x^{1}\times 4x^{0}+4x^{0}\right)}{\left(4x^{1}-5\right)^{2}}$$

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

$$\frac{4\times 32x^{1+1}+4\left(-20\right)x^{1}-5\times 32x^{1}-5\left(-20\right)x^{0}-\left(16\times 4x^{2}-20\times 4x^{1}+4x^{0}\right)}{\left(4x^{1}-5\right)^{2}}$$

Qisqartirish.

$$\frac{128x^{2}-80x^{1}-160x^{1}+100x^{0}-\left(64x^{2}-80x^{1}+4x^{0}\right)}{\left(4x^{1}-5\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{64x^{2}-160x^{1}+96x^{0}}{\left(4x^{1}-5\right)^{2}}$$

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

$$\frac{64x^{2}-160x+96x^{0}}{\left(4x-5\right)^{2}}$$

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

$$\frac{64x^{2}-160x+96\times 1}{\left(4x-5\right)^{2}}$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{64x^{2}-160x+96}{\left(4x-5\right)^{2}}$$