6x/9y*3y/2x^5 eching

$$\frac { 6 x } { 9 y } \cdot \frac { 3 y } { 2 x ^ { 5 } }$$

Baholash

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

Yechim qadamlari

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{2x}{3y}\times \frac{3y}{2x^{5}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2x}{3y} ni \frac{3y}{2x^{5}} ga ko‘paytiring.

$$\frac{2x\times 3y}{3y\times 2x^{5}}$$

Surat va maxrajdagi ikkala 2\times 3xy ni qisqartiring.

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

x ga nisbatan hosilani topish

$$-\frac{4}{x^{5}}$$

Zanjirli qoidadan foydalanish qadamalari

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x}{3y}\times \frac{3y}{2x^{5}})$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2x}{3y} ni \frac{3y}{2x^{5}} ga ko‘paytiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\times 3y}{3y\times 2x^{5}})$$

Surat va maxrajdagi ikkala 2\times 3xy ni qisqartiring.

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

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.

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

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

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

Qisqartirish.

$$-4x^{3}\left(x^{4}\right)^{-2}$$