1/y{frac{1/2x}}*1/2x/frac{1{y}} eching

$$\frac{ 1 }{ \frac{ y }{ \frac{ 1 }{ 2x } } } \times \frac{ \frac{ 1 }{ 2x } }{ \frac{ 1 }{ y } }$$

Baholash

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

Yechim qadamlari

1 ni \frac{y}{\frac{1}{2x}} ga bo'lish 1 ga k'paytirish \frac{y}{\frac{1}{2x}} ga qaytarish.

$$\frac{\frac{1}{2x}}{y}\times \frac{\frac{1}{2x}}{\frac{1}{y}}$$

\frac{\frac{1}{2x}}{y} ni yagona kasrga aylantiring.

$$\frac{1}{2xy}\times \frac{\frac{1}{2x}}{\frac{1}{y}}$$

\frac{1}{2x} ni \frac{1}{y} ga bo'lish \frac{1}{2x} ga k'paytirish \frac{1}{y} ga qaytarish.

$$\frac{1}{2xy}\times \frac{y}{2x}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{2xy} ni \frac{y}{2x} ga ko‘paytiring.

$$\frac{y}{2xy\times 2x}$$

Surat va maxrajdagi ikkala y ni qisqartiring.

$$\frac{1}{2\times 2xx}$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\frac{1}{2\times 2x^{2}}$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

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

x ga nisbatan hosilani topish

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

Zanjirli qoidadan foydalanish qadamalari

1 ni \frac{y}{\frac{1}{2x}} ga bo'lish 1 ga k'paytirish \frac{y}{\frac{1}{2x}} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{2x}}{y}\times \frac{\frac{1}{2x}}{\frac{1}{y}})$$

\frac{\frac{1}{2x}}{y} ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2xy}\times \frac{\frac{1}{2x}}{\frac{1}{y}})$$

\frac{1}{2x} ni \frac{1}{y} ga bo'lish \frac{1}{2x} ga k'paytirish \frac{1}{y} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2xy}\times \frac{y}{2x})$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{2xy} ni \frac{y}{2x} ga ko‘paytiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y}{2xy\times 2x})$$

Surat va maxrajdagi ikkala y ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2\times 2xx})$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

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

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.

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

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

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

Qisqartirish.

$$-8x^{1}\times \left(4x^{2}\right)^{-2}$$

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

$$-8x\times \left(4x^{2}\right)^{-2}$$