d/dxleft(1/x(x-y)right) eching

$$\frac{d}{d x } \left( \frac{ 1 }{ x(x-y) } \right)$$

Baholash

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

Zanjirli qoidadan foydalanish qadamalari

x ga x-y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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.

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

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

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

Qisqartirish.

$$\left(x^{2}+\left(-y\right)x^{1}\right)^{-2}\left(-2x^{1}+yx^{0}\right)$$

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

$$\left(x^{2}+\left(-y\right)x\right)^{-2}\left(-2x+yx^{0}\right)$$

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

$$\left(x^{2}+\left(-y\right)x\right)^{-2}\left(-2x+y\times 1\right)$$

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

$$\left(x^{2}+\left(-y\right)x\right)^{-2}\left(-2x+y\right)$$

x ga nisbatan hosilani topish

$$\frac{2\left(3x^{2}-3xy+y^{2}\right)}{\left(x\left(x-y\right)\right)^{3}}$$