x^4*-1/x eching

$${ x }^{ 4 } \times - \frac{ 1 }{ x }$$

Baholash

$$-x^{3}$$

Yechim qadamlari

x^{4}\left(-\frac{1}{x}\right) ni yagona kasrga aylantiring.

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

Surat va maxrajdagi ikkala x ni qisqartiring.

$$-x^{3}$$

x ga nisbatan hosilani topish

$$-3x^{2}$$

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.

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

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

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

Qisqartirish.

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

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

$$x^{4-2}-4x^{-1+3}$$

Qisqartirish.

$$x^{2}-4x^{2}$$