Đáp án + Giải thích các bước giải:

$y = \dfrac{1}{3}\sqrt{200 - 10\sqrt{2}x} \cdot x^2$ 

$\Rightarrow y' = \dfrac{1}{3}\big[\big(\sqrt{200 - 10\sqrt{2}x}\big)'\cdot x^2 + \big(\sqrt{200 - 10\sqrt{2}x}\big)(x^2)'\big]$

$= \dfrac{1}{3}\bigg[\dfrac{-5\sqrt{2}}{\sqrt{200 - 10\sqrt{2}x}} \cdot x^2 + \sqrt{200 - 10\sqrt{2}x} \cdot 2x \bigg]$

$= \dfrac{1}{3}\bigg[\dfrac{-5\sqrt{2}x^2}{\sqrt{200 - 10\sqrt{2}x}} + 2x\sqrt{200 - 10\sqrt{2}x}\bigg]$

$= \dfrac{1}{3} \cdot \dfrac{2x(200 - 10\sqrt{2}x) - 5\sqrt{2}x^2}{\sqrt{200 - 10\sqrt{2}x}}$

$= \dfrac{1}{3} \cdot \dfrac{400x - 20\sqrt{2}x^2 - 5\sqrt{2}x^2}{\sqrt{200 - 10\sqrt{2}x}}$

$= \dfrac{400x - 25\sqrt{2}x^2}{3\sqrt{200 - 10\sqrt{2}x}}$