v/v^2+17v+72-8/v^2+15v+56 eching

$$\frac { v } { v ^ { 2 } + 17 v + 72 } - \frac { 8 } { v ^ { 2 } + 15 v + 56 }$$

Baholash

$$\frac{v-9}{\left(v+7\right)\left(v+9\right)}$$

Qisqa yechim qadamlari

Faktor: v^{2}+17v+72. Faktor: v^{2}+15v+56.

$$\frac{v}{\left(v+8\right)\left(v+9\right)}-\frac{8}{\left(v+7\right)\left(v+8\right)}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(v+8\right)\left(v+9\right) va \left(v+7\right)\left(v+8\right) ning eng kichik umumiy karralisi \left(v+7\right)\left(v+8\right)\left(v+9\right). \frac{v}{\left(v+8\right)\left(v+9\right)} ni \frac{v+7}{v+7} marotabaga ko'paytirish. \frac{8}{\left(v+7\right)\left(v+8\right)} ni \frac{v+9}{v+9} marotabaga ko'paytirish.

$$\frac{v\left(v+7\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}-\frac{8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}$$

\frac{v\left(v+7\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)} va \frac{8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{v\left(v+7\right)-8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}$$

v\left(v+7\right)-8\left(v+9\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{v^{2}+7v-8v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}$$

v^{2}+7v-8v-72 kabi iboralarga o‘xshab birlashtiring.

$$\frac{v^{2}-v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}$$

\frac{v^{2}-v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\left(v-9\right)\left(v+8\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}$$

Surat va maxrajdagi ikkala v+8 ni qisqartiring.

$$\frac{v-9}{\left(v+7\right)\left(v+9\right)}$$

\left(v+7\right)\left(v+9\right) ni kengaytirish.

$$\frac{v-9}{v^{2}+16v+63}$$

v ga nisbatan hosilani topish

$$\frac{207+18v-v^{2}}{v^{4}+32v^{3}+382v^{2}+2016v+3969}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Faktor: v^{2}+17v+72. Faktor: v^{2}+15v+56.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v}{\left(v+8\right)\left(v+9\right)}-\frac{8}{\left(v+7\right)\left(v+8\right)})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(v+8\right)\left(v+9\right) va \left(v+7\right)\left(v+8\right) ning eng kichik umumiy karralisi \left(v+7\right)\left(v+8\right)\left(v+9\right). \frac{v}{\left(v+8\right)\left(v+9\right)} ni \frac{v+7}{v+7} marotabaga ko'paytirish. \frac{8}{\left(v+7\right)\left(v+8\right)} ni \frac{v+9}{v+9} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v\left(v+7\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)}-\frac{8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)})$$

\frac{v\left(v+7\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)} va \frac{8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v\left(v+7\right)-8\left(v+9\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)})$$

v\left(v+7\right)-8\left(v+9\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}+7v-8v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)})$$

v^{2}+7v-8v-72 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v^{2}-v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)})$$

\frac{v^{2}-v-72}{\left(v+7\right)\left(v+8\right)\left(v+9\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{\left(v-9\right)\left(v+8\right)}{\left(v+7\right)\left(v+8\right)\left(v+9\right)})$$

Surat va maxrajdagi ikkala v+8 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v-9}{\left(v+7\right)\left(v+9\right)})$$

v+7 ga v+9 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v-9}{v^{2}+16v+63})$$

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

$$\frac{\left(v^{2}+16v^{1}+63\right)\frac{\mathrm{d}}{\mathrm{d}v}(v^{1}-9)-\left(v^{1}-9\right)\frac{\mathrm{d}}{\mathrm{d}v}(v^{2}+16v^{1}+63)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

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

$$\frac{\left(v^{2}+16v^{1}+63\right)v^{1-1}-\left(v^{1}-9\right)\left(2v^{2-1}+16v^{1-1}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

Qisqartirish.

$$\frac{\left(v^{2}+16v^{1}+63\right)v^{0}-\left(v^{1}-9\right)\left(2v^{1}+16v^{0}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

v^{2}+16v^{1}+63 ni v^{0} marotabaga ko'paytirish.

$$\frac{v^{2}v^{0}+16v^{1}v^{0}+63v^{0}-\left(v^{1}-9\right)\left(2v^{1}+16v^{0}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

v^{1}-9 ni 2v^{1}+16v^{0} marotabaga ko'paytirish.

$$\frac{v^{2}v^{0}+16v^{1}v^{0}+63v^{0}-\left(v^{1}\times 2v^{1}+v^{1}\times 16v^{0}-9\times 2v^{1}-9\times 16v^{0}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

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

$$\frac{v^{2}+16v^{1}+63v^{0}-\left(2v^{1+1}+16v^{1}-9\times 2v^{1}-9\times 16v^{0}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

Qisqartirish.

$$\frac{v^{2}+16v^{1}+63v^{0}-\left(2v^{2}+16v^{1}-18v^{1}-144v^{0}\right)}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-v^{2}+18v^{1}+207v^{0}}{\left(v^{2}+16v^{1}+63\right)^{2}}$$

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

$$\frac{-v^{2}+18v+207v^{0}}{\left(v^{2}+16v+63\right)^{2}}$$

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

$$\frac{-v^{2}+18v+207\times 1}{\left(v^{2}+16v+63\right)^{2}}$$

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

$$\frac{-v^{2}+18v+207}{\left(v^{2}+16v+63\right)^{2}}$$