x^2({x}^frac{1{2}}) eching

$${ x }^{ 2 } ( { x }^{ \frac{ 1 }{ 2 } } )$$

x ga nisbatan hosilani topish

$$\frac{5x^{\frac{3}{2}}}{2}$$

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.

$$x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(\sqrt{x})+\sqrt{x}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2})$$

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

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

Qisqartirish.

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

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

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

Qisqartirish.

$$\frac{1}{2}x^{\frac{3}{2}}+2x^{\frac{3}{2}}$$

Baholash

$$x^{\frac{5}{2}}$$