s^frac{5{12}}*s^frac{16{9}} eching

$$s ^ { \frac { 5 } { 12 } } \cdot s ^ { \frac { 16 } { 9 } }$$

s ga nisbatan hosilani topish

$$\frac{79s^{\frac{43}{36}}}{36}$$

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.

$$s^{\frac{5}{12}}\frac{\mathrm{d}}{\mathrm{d}s}(s^{\frac{16}{9}})+s^{\frac{16}{9}}\frac{\mathrm{d}}{\mathrm{d}s}(s^{\frac{5}{12}})$$

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

$$s^{\frac{5}{12}}\times \frac{16}{9}s^{\frac{16}{9}-1}+s^{\frac{16}{9}}\times \frac{5}{12}s^{\frac{5}{12}-1}$$

Qisqartirish.

$$s^{\frac{5}{12}}\times \frac{16}{9}s^{\frac{7}{9}}+s^{\frac{16}{9}}\times \frac{5}{12}s^{-\frac{7}{12}}$$

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

$$\frac{16}{9}s^{\frac{5}{12}+\frac{7}{9}}+\frac{5}{12}s^{\frac{16}{9}-\frac{7}{12}}$$

Qisqartirish.

$$\frac{16}{9}s^{\frac{43}{36}}+\frac{5}{12}s^{\frac{43}{36}}$$

Baholash

$$s^{\frac{79}{36}}$$