(frac{6f^{2}g^-8h^2}{32fg^-5h^4}) eching

$$( \frac { 6 f ^ { 2 } g ^ { - 8 } h ^ { 2 } } { 32 f g ^ { - 5 } h ^ { 4 } } )$$

Baholash

$$\frac{3f}{16h^{2}g^{3}}$$

Yechim qadamlari

Surat va maxrajdagi ikkala 2fh^{2} ni qisqartiring.

$$\frac{3g^{-8}f}{16g^{-5}h^{2}}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\frac{3f}{16h^{2}g^{3}}$$

f ga nisbatan hosilani topish

$$\frac{3}{16h^{2}g^{3}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{6h^{2}}{g^{8}\times \frac{32h^{4}}{g^{5}}}f^{2-1})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{3}{16h^{2}g^{3}}f^{1})$$

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

$$\frac{3}{16h^{2}g^{3}}f^{1-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{3}{16h^{2}g^{3}}f^{0}$$

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

$$\frac{3}{16h^{2}g^{3}}\times 1$$

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

$$\frac{3}{16h^{2}g^{3}}$$