{x}^-frac{1{4}}({x}^-frac{1{2}}) eching

$${ x }^{ - \frac{ 1 }{ 4 } } ( { x }^{ - \frac{ 1 }{ 2 } } )$$

x ga nisbatan hosilani topish

$$-\frac{3}{4x^{\frac{7}{4}}}$$

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.

$$x^{-\frac{1}{4}}\frac{\mathrm{d}}{\mathrm{d}x}(x^{-\frac{1}{2}})+x^{-\frac{1}{2}}\frac{\mathrm{d}}{\mathrm{d}x}(x^{-\frac{1}{4}})$$

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

$$x^{-\frac{1}{4}}\left(-\frac{1}{2}\right)x^{-\frac{1}{2}-1}+x^{-\frac{1}{2}}\left(-\frac{1}{4}\right)x^{-\frac{1}{4}-1}$$

Qisqartirish.

$$x^{-\frac{1}{4}}\left(-\frac{1}{2}\right)x^{-\frac{3}{2}}+x^{-\frac{1}{2}}\left(-\frac{1}{4}\right)x^{-\frac{5}{4}}$$

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

$$-\frac{1}{2}x^{-\frac{1}{4}-\frac{3}{2}}-\frac{1}{4}x^{-\frac{1}{2}-\frac{5}{4}}$$

Qisqartirish.

$$-\frac{1}{2}x^{-\frac{7}{4}}-\frac{1}{4}x^{-\frac{7}{4}}$$

Baholash

$$\frac{1}{x^{\frac{3}{4}}}$$