x*x^frac{4{8}} eching

$$x \times x ^ { \frac { 4 } { 8 } }$$

x ga nisbatan hosilani topish

$$\frac{3\sqrt{x}}{2}$$

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.

$$x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(\sqrt{x})+\sqrt{x}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})$$

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

$$x^{1}\times \frac{1}{2}x^{\frac{1}{2}-1}+\sqrt{x}x^{1-1}$$

Qisqartirish.

$$x^{1}\times \frac{1}{2}x^{-\frac{1}{2}}+\sqrt{x}x^{0}$$

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

$$\frac{1}{2}x^{1-\frac{1}{2}}+x^{\frac{1}{2}}$$

Qisqartirish.

$$\frac{1}{2}\sqrt{x}+\sqrt{x}$$

Baholash

$$x^{\frac{3}{2}}$$