Монгол Бодлогын Сан

Заавар:

Бодолт: \begin{align*} f'(x)&=\left( \left( {\sqrt[{3}]{{x}} - 2\sqrt {x}} \right)^{3}\right)'\\ &=3\left( {\sqrt[{3}]{{x}} - 2\sqrt {x}} \right)^{2}\cdot \left( {\sqrt[{3}]{{x}} - 2\sqrt {x}} \right)'\\ &=3\left( {\sqrt[{3}]{{x}} - 2\sqrt {x}} \right)^{2}\cdot\Big(\dfrac{1}{3\sqrt[3]{x^2}}-2\cdot\dfrac{1}{2\sqrt{x}}\Big)\\ &=\left(x^{\frac13}-2x^{\frac12}\right)^{2}\cdot\left(x^{-\frac23}-3x^{-\frac12}\right)\\ &=\left(x^{\frac23}-4x^{\frac56}+4x\right)\cdot\left(x^{-\frac23}-3x^{-\frac12}\right)\\ &=1-3x^{\frac16}-4x^{\frac16}+12x^{\frac13}+4x^{\frac13}-12x^{\frac12}\\ &=1-7x^{\frac16}+16x^{\frac13}-12x^{\frac12}\\ \end{align*}