f(x)=(x-1)^2/3 eching

$$f ( x ) = ( x - 1 ) ^ { 2 / 3 }$$

x ga nisbatan hosilani topish

$$\frac{2}{3\sqrt[3]{x-1}}$$

Zanjirli qoidadan foydalanish qadamalari

Agar F ikki differensial funksiya f\left(u\right) va u=g\left(x\right)'ning yig'indisi bo'lsa, ya'ni agar F\left(x\right)=f\left(g\left(x\right)\right) bo'lsa, F hosilasi f'ning u martalik hosilasi, g'ning x martalik hosilasi ya'ni \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right) bo'ladi.

$$\frac{2}{3}\left(x^{1}-1\right)^{\frac{2}{3}-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-1)$$

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

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

Qisqartirish.

$$\frac{2}{3}x^{0}\left(x^{1}-1\right)^{-\frac{1}{3}}$$

Har qanday t sharti uchun t^{1}=t.

$$\frac{2}{3}x^{0}\left(x-1\right)^{-\frac{1}{3}}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$\frac{2}{3}\times 1\left(x-1\right)^{-\frac{1}{3}}$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

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

Baholash

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