2/y^2-16-3/y+4 eching

$$\frac { 2 } { y ^ { 2 } - 16 } - \frac { 3 } { y + 4 }$$

Baholash

$$\frac{14-3y}{y^{2}-16}$$

Qisqa yechim qadamlari

Faktor: y^{2}-16.

$$\frac{2}{\left(y-4\right)\left(y+4\right)}-\frac{3}{y+4}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(y-4\right)\left(y+4\right) va y+4 ning eng kichik umumiy karralisi \left(y-4\right)\left(y+4\right). \frac{3}{y+4} ni \frac{y-4}{y-4} marotabaga ko'paytirish.

$$\frac{2}{\left(y-4\right)\left(y+4\right)}-\frac{3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)}$$

\frac{2}{\left(y-4\right)\left(y+4\right)} va \frac{3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2-3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)}$$

2-3\left(y-4\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{2-3y+12}{\left(y-4\right)\left(y+4\right)}$$

2-3y+12 kabi iboralarga o‘xshab birlashtiring.

$$\frac{14-3y}{\left(y-4\right)\left(y+4\right)}$$

\left(y-4\right)\left(y+4\right) ni kengaytirish.

$$\frac{14-3y}{y^{2}-16}$$

y ga nisbatan hosilani topish

$$\frac{3y^{2}-28y+48}{\left(y^{2}-16\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Faktor: y^{2}-16.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2}{\left(y-4\right)\left(y+4\right)}-\frac{3}{y+4})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(y-4\right)\left(y+4\right) va y+4 ning eng kichik umumiy karralisi \left(y-4\right)\left(y+4\right). \frac{3}{y+4} ni \frac{y-4}{y-4} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2}{\left(y-4\right)\left(y+4\right)}-\frac{3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)})$$

\frac{2}{\left(y-4\right)\left(y+4\right)} va \frac{3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2-3\left(y-4\right)}{\left(y-4\right)\left(y+4\right)})$$

2-3\left(y-4\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2-3y+12}{\left(y-4\right)\left(y+4\right)})$$

2-3y+12 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{14-3y}{\left(y-4\right)\left(y+4\right)})$$

Hisoblang: \left(y-4\right)\left(y+4\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 4 kvadratini chiqarish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{14-3y}{y^{2}-16})$$

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

$$\frac{\left(y^{2}-16\right)\frac{\mathrm{d}}{\mathrm{d}y}(-3y^{1}+14)-\left(-3y^{1}+14\right)\frac{\mathrm{d}}{\mathrm{d}y}(y^{2}-16)}{\left(y^{2}-16\right)^{2}}$$

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

$$\frac{\left(y^{2}-16\right)\left(-3\right)y^{1-1}-\left(-3y^{1}+14\right)\times 2y^{2-1}}{\left(y^{2}-16\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(y^{2}-16\right)\left(-3\right)y^{0}-\left(-3y^{1}+14\right)\times 2y^{1}}{\left(y^{2}-16\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{y^{2}\left(-3\right)y^{0}-16\left(-3\right)y^{0}-\left(-3y^{1}\times 2y^{1}+14\times 2y^{1}\right)}{\left(y^{2}-16\right)^{2}}$$

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

$$\frac{-3y^{2}-16\left(-3\right)y^{0}-\left(-3\times 2y^{1+1}+14\times 2y^{1}\right)}{\left(y^{2}-16\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{-3y^{2}+48y^{0}-\left(-6y^{2}+28y^{1}\right)}{\left(y^{2}-16\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{-3y^{2}+48y^{0}-\left(-6y^{2}\right)-28y^{1}}{\left(y^{2}-16\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-3-\left(-6\right)\right)y^{2}+48y^{0}-28y^{1}}{\left(y^{2}-16\right)^{2}}$$

-3 dan -6 ni ayirish.

$$\frac{3y^{2}+48y^{0}-28y^{1}}{\left(y^{2}-16\right)^{2}}$$

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

$$\frac{3y^{2}+48y^{0}-28y}{\left(y^{2}-16\right)^{2}}$$

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

$$\frac{3y^{2}+48\times 1-28y}{\left(y^{2}-16\right)^{2}}$$

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

$$\frac{3y^{2}+48-28y}{\left(y^{2}-16\right)^{2}}$$