Il faut calculer f'(x): f (x) = (2 – x)* √x

Bonjour Steph23

[tex]f(x)=(2-x) \sqrt{x}\\\\f'(x)=(2-x)'\times \sqrt{x}+(2-x)\times(\sqrt{x})'\\\\f'(x)=(-1)\times\sqrt{x} +(2-x)\times\dfrac{1}{2 \sqrt{x}}\\\\f'(x)=-\sqrt{x} + \dfrac{2-x}{2\sqrt{x}}\\\\f'(x)= \dfrac{-\sqrt{x}\times2 \sqrt{x}}{2 \sqrt{x} }+\dfrac{2-x}{2 \sqrt{x}}\\\\f'(x)= \dfrac{-2x}{2 \sqrt{x} }+\dfrac{2-x}{2 \sqrt{x} } [/tex]

[tex]\\\\f'(x)=\dfrac{-2x+2-x}{2\sqrt{x}}\\\\\boxed{f'(x)=\dfrac{-3x+2}{2\sqrt{x}}}[/tex]