x^2*x*x^3/xfrac{1{2}*x*x1/3} eching

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

Baholash

$$6x^{3}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\frac{x^{3}x^{3}}{x\times \frac{1}{2}xx\times \frac{1}{3}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 3 ni qo‘shib, 6 ni oling.

$$\frac{x^{6}}{x\times \frac{1}{2}xx\times \frac{1}{3}}$$

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

$$\frac{x^{6}}{x^{2}\times \frac{1}{2}x\times \frac{1}{3}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\frac{x^{6}}{x^{3}\times \frac{1}{2}\times \frac{1}{3}}$$

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

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

\frac{1}{6} hosil qilish uchun \frac{1}{3} va \frac{1}{2} ni ko'paytirish.

$$\frac{x^{3}}{\frac{1}{6}}$$

x^{3} ni \frac{1}{6} ga bo'lish x^{3} ga k'paytirish \frac{1}{6} ga qaytarish.

$$x^{3}\times 6$$

x ga nisbatan hosilani topish

$$18x^{2}$$

Yechim qadamlari

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}x^{1})$$

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

$$6x^{2}x^{1-1}$$

Arifmetik hisobni amalga oshirish.

$$6x^{2}x^{0}$$

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

$$6x^{2}\times 1$$

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

$$6x^{2}$$