2r/r+10+5 eching

$$\frac { 2 r } { r + 10 } + 5$$

Baholash

$$\frac{7r+50}{r+10}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 ni \frac{r+10}{r+10} marotabaga ko'paytirish.

$$\frac{2r}{r+10}+\frac{5\left(r+10\right)}{r+10}$$

\frac{2r}{r+10} va \frac{5\left(r+10\right)}{r+10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2r+5\left(r+10\right)}{r+10}$$

2r+5\left(r+10\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{2r+5r+50}{r+10}$$

2r+5r+50 kabi iboralarga o‘xshab birlashtiring.

$$\frac{7r+50}{r+10}$$

r ga nisbatan hosilani topish

$$\frac{20}{\left(r+10\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 ni \frac{r+10}{r+10} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r}{r+10}+\frac{5\left(r+10\right)}{r+10})$$

\frac{2r}{r+10} va \frac{5\left(r+10\right)}{r+10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r+5\left(r+10\right)}{r+10})$$

2r+5\left(r+10\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2r+5r+50}{r+10})$$

2r+5r+50 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{7r+50}{r+10})$$

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

$$\frac{\left(r^{1}+10\right)\frac{\mathrm{d}}{\mathrm{d}r}(7r^{1}+50)-\left(7r^{1}+50\right)\frac{\mathrm{d}}{\mathrm{d}r}(r^{1}+10)}{\left(r^{1}+10\right)^{2}}$$

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

$$\frac{\left(r^{1}+10\right)\times 7r^{1-1}-\left(7r^{1}+50\right)r^{1-1}}{\left(r^{1}+10\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(r^{1}+10\right)\times 7r^{0}-\left(7r^{1}+50\right)r^{0}}{\left(r^{1}+10\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{r^{1}\times 7r^{0}+10\times 7r^{0}-\left(7r^{1}r^{0}+50r^{0}\right)}{\left(r^{1}+10\right)^{2}}$$

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

$$\frac{7r^{1}+10\times 7r^{0}-\left(7r^{1}+50r^{0}\right)}{\left(r^{1}+10\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{7r^{1}+70r^{0}-\left(7r^{1}+50r^{0}\right)}{\left(r^{1}+10\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{7r^{1}+70r^{0}-7r^{1}-50r^{0}}{\left(r^{1}+10\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(7-7\right)r^{1}+\left(70-50\right)r^{0}}{\left(r^{1}+10\right)^{2}}$$

7 dan 7 ni va 70 dan 50 ni ayiring.

$$\frac{20r^{0}}{\left(r^{1}+10\right)^{2}}$$

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

$$\frac{20r^{0}}{\left(r+10\right)^{2}}$$

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

$$\frac{20\times 1}{\left(r+10\right)^{2}}$$

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

$$\frac{20}{\left(r+10\right)^{2}}$$