(6/5x^{5}y^{4}z^8):(5/3x^3y^3z^7)= eching

$$( \frac { 6 } { 5 } x ^ { 5 } y ^ { 4 } z ^ { 8 } ) : ( \frac { 5 } { 3 } x ^ { 3 } y ^ { 3 } z ^ { 7 } ) =$$

Baholash

$$\frac{18yzx^{2}}{25}$$

Yechim qadamlari

Surat va maxrajdagi ikkala x^{3}y^{3}z^{7} ni qisqartiring.

$$\frac{\frac{6}{5}yzx^{2}}{\frac{5}{3}}$$

\frac{6}{5}yzx^{2} ni \frac{5}{3} ga bo'lish \frac{6}{5}yzx^{2} ga k'paytirish \frac{5}{3} ga qaytarish.

$$\frac{\frac{6}{5}yzx^{2}\times 3}{5}$$

\frac{18}{5} hosil qilish uchun \frac{6}{5} va 3 ni ko'paytirish.

$$\frac{\frac{18}{5}yzx^{2}}{5}$$

\frac{18}{25}yzx^{2} ni olish uchun \frac{18}{5}yzx^{2} ni 5 ga bo‘ling.

$$\frac{18}{25}yzx^{2}$$

x ga nisbatan hosilani topish

$$\frac{36xyz}{25}$$

Yechim qadamlari

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{4}z^{8}}{5\times \frac{5y^{3}z^{7}}{3}}x^{5-3})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18yz}{25}x^{2})$$

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

$$2\times \frac{18yz}{25}x^{2-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{36yz}{25}x^{1}$$

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

$$\frac{36yz}{25}x$$