frac{{left(sqrt{x^4}right)}^{2}*{left(sqrt{x^8}right)}^{2}{left(sqrt{x^14}right)}^{2}}{{left(sqrt{x^4}right)}^{2}*{left(sqrt{{x}^8}right)}^2*{left(sqrt{{x}^2}right)}^2} eching

$$\frac{ { \left( \sqrt{ { x }^{ 4 } } \right) }^{ 2 } \times { \left( \sqrt{ { x }^{ 8 } } \right) }^{ 2 } { \left( \sqrt{ { x }^{ 14 } } \right) }^{ 2 } }{ { \left( \sqrt{ { x }^{ 4 } } \right) }^{ 2 } \times { \left( \sqrt{ { x }^{ 8 } } \right) }^{ 2 } \times { \left( \sqrt{ { x }^{ 2 } } \right) }^{ 2 } }$$

Baholash

$$x^{12}$$

Yechim qadamlari

Surat va maxrajdagi ikkala \left(\sqrt{x^{4}}\right)^{2}\left(\sqrt{x^{8}}\right)^{2} ni qisqartiring.

$$\frac{\left(\sqrt{x^{14}}\right)^{2}}{\left(\sqrt{x^{2}}\right)^{2}}$$

2 daraja ko‘rsatkichini \sqrt{x^{14}} ga hisoblang va x^{14} ni qiymatni oling.

$$\frac{x^{14}}{\left(\sqrt{x^{2}}\right)^{2}}$$

2 daraja ko‘rsatkichini \sqrt{x^{2}} ga hisoblang va x^{2} ni qiymatni oling.

$$\frac{x^{14}}{x^{2}}$$

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

$$x^{12}$$

x ga nisbatan hosilani topish

$$12x^{11}$$

Derivativ ifodasidan foydalanish qadamlari

Surat va maxrajdagi ikkala \left(\sqrt{x^{4}}\right)^{2}\left(\sqrt{x^{8}}\right)^{2} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(\sqrt{x^{14}}\right)^{2}}{\left(\sqrt{x^{2}}\right)^{2}})$$

2 daraja ko‘rsatkichini \sqrt{x^{14}} ga hisoblang va x^{14} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{14}}{\left(\sqrt{x^{2}}\right)^{2}})$$

2 daraja ko‘rsatkichini \sqrt{x^{2}} ga hisoblang va x^{2} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{14}}{x^{2}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{12})$$

ax^{n} hosilasi – nax^{n-1}.

$$12x^{12-1}$$

12 dan 1 ni ayirish.

$$12x^{11}$$