Question

f(x) =(x-rad.x)^3
Sa se calculeze derivata funcției f.
Va rog. Mulțumesc!

Answer 1

$\displaystyle\bf\\f(x) =(x-\sqrt x)^3\\\\f'(x)=\Big((x-\sqrt x)^3\Big)'\\\\Folosim~formula:\\\\\Big(u^n\Big)'=n\cdot u^{n-1}\cdot u'\\\\\left(\Big(x-\sqrt x\Big)^3\right)'=3\cdot \Big(x-\sqrt x\Big)^{3-1}\cdot\Big(x-\sqrt x\Big)'=\\\\=3\cdot \Big(x-\sqrt x\Big)^2\cdot\Big(1-\frac{1}{2\sqrt{x}} \Big)$