(k/3)(k/4) eching

$$( \frac { k } { 3 } ) ( \frac { k } { 4 } )$$

Baholash

$$\frac{k^{2}}{12}$$

Yechim qadamlari

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{k}{3} ni \frac{k}{4} ga ko‘paytiring.

$$\frac{kk}{3\times 4}$$

k^{2} hosil qilish uchun k va k ni ko'paytirish.

$$\frac{k^{2}}{3\times 4}$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$\frac{k^{2}}{12}$$

k ga nisbatan hosilani topish

$$\frac{k}{6}$$

Koʻpaytma uchun derivativ qoidasidan foydalanish qadamlari

Har qanday ikki differensial funksiya uchun, ikki funksiya koʻpaytmasining hosilasi birinchi funksiya marotabasi, ikkinchi plyus hosilasi ikkinchi funksiya marotabasi birinchining hosilasidir.

$$\frac{1}{3}k^{1}\frac{\mathrm{d}}{\mathrm{d}k}(\frac{1}{4}k^{1})+\frac{1}{4}k^{1}\frac{\mathrm{d}}{\mathrm{d}k}(\frac{1}{3}k^{1})$$

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

$$\frac{1}{3}k^{1}\times \frac{1}{4}k^{1-1}+\frac{1}{4}k^{1}\times \frac{1}{3}k^{1-1}$$

Qisqartirish.

$$\frac{1}{3}k^{1}\times \frac{1}{4}k^{0}+\frac{1}{4}k^{1}\times \frac{1}{3}k^{0}$$

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

$$\frac{1}{4}\times \frac{1}{3}k^{1}+\frac{1}{4}\times \frac{1}{3}k^{1}$$

Qisqartirish.

$$\frac{1}{12}k^{1}+\frac{1}{12}k^{1}$$

O'xshash hadlarni birlashtirish.

$$\frac{1+1}{12}k^{1}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{12} ni \frac{1}{12} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$\frac{1}{6}k^{1}$$

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

$$\frac{1}{6}k$$