7/w^2-9+2/w-3 eching

$$\frac { 7 } { w ^ { 2 } - 9 } + \frac { 2 } { w - 3 }$$

Baholash

$$\frac{2w+13}{w^{2}-9}$$

Qisqa yechim qadamlari

Faktor: w^{2}-9.

$$\frac{7}{\left(w-3\right)\left(w+3\right)}+\frac{2}{w-3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(w-3\right)\left(w+3\right) va w-3 ning eng kichik umumiy karralisi \left(w-3\right)\left(w+3\right). \frac{2}{w-3} ni \frac{w+3}{w+3} marotabaga ko'paytirish.

$$\frac{7}{\left(w-3\right)\left(w+3\right)}+\frac{2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)}$$

\frac{7}{\left(w-3\right)\left(w+3\right)} va \frac{2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{7+2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)}$$

7+2\left(w+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{7+2w+6}{\left(w-3\right)\left(w+3\right)}$$

7+2w+6 kabi iboralarga o‘xshab birlashtiring.

$$\frac{13+2w}{\left(w-3\right)\left(w+3\right)}$$

\left(w-3\right)\left(w+3\right) ni kengaytirish.

$$\frac{13+2w}{w^{2}-9}$$

w ga nisbatan hosilani topish

$$-\frac{2\left(w^{2}+13w+9\right)}{\left(w^{2}-9\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Faktor: w^{2}-9.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{7}{\left(w-3\right)\left(w+3\right)}+\frac{2}{w-3})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(w-3\right)\left(w+3\right) va w-3 ning eng kichik umumiy karralisi \left(w-3\right)\left(w+3\right). \frac{2}{w-3} ni \frac{w+3}{w+3} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{7}{\left(w-3\right)\left(w+3\right)}+\frac{2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)})$$

\frac{7}{\left(w-3\right)\left(w+3\right)} va \frac{2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{7+2\left(w+3\right)}{\left(w-3\right)\left(w+3\right)})$$

7+2\left(w+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{7+2w+6}{\left(w-3\right)\left(w+3\right)})$$

7+2w+6 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{13+2w}{\left(w-3\right)\left(w+3\right)})$$

Hisoblang: \left(w-3\right)\left(w+3\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{13+2w}{w^{2}-9})$$

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

$$\frac{\left(w^{2}-9\right)\frac{\mathrm{d}}{\mathrm{d}w}(2w^{1}+13)-\left(2w^{1}+13\right)\frac{\mathrm{d}}{\mathrm{d}w}(w^{2}-9)}{\left(w^{2}-9\right)^{2}}$$

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

$$\frac{\left(w^{2}-9\right)\times 2w^{1-1}-\left(2w^{1}+13\right)\times 2w^{2-1}}{\left(w^{2}-9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(w^{2}-9\right)\times 2w^{0}-\left(2w^{1}+13\right)\times 2w^{1}}{\left(w^{2}-9\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{w^{2}\times 2w^{0}-9\times 2w^{0}-\left(2w^{1}\times 2w^{1}+13\times 2w^{1}\right)}{\left(w^{2}-9\right)^{2}}$$

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

$$\frac{2w^{2}-9\times 2w^{0}-\left(2\times 2w^{1+1}+13\times 2w^{1}\right)}{\left(w^{2}-9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{2w^{2}-18w^{0}-\left(4w^{2}+26w^{1}\right)}{\left(w^{2}-9\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{2w^{2}-18w^{0}-4w^{2}-26w^{1}}{\left(w^{2}-9\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(2-4\right)w^{2}-18w^{0}-26w^{1}}{\left(w^{2}-9\right)^{2}}$$

2 dan 4 ni ayirish.

$$\frac{-2w^{2}-18w^{0}-26w^{1}}{\left(w^{2}-9\right)^{2}}$$

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

$$\frac{-2w^{2}-18w^{0}-26w}{\left(w^{2}-9\right)^{2}}$$

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

$$\frac{-2w^{2}-18-26w}{\left(w^{2}-9\right)^{2}}$$