Question

Imi puteti explica va rog pe pasi cum ar trebui sa fac derivata asta ?

Answer 1

Cand derivezi $(\frac{u(x)}{w(x)} )'=\frac{u'(x)w(x)-u(x)w'(x)}{w^2(x)}$
(derivata fractiei este (numarator derivat ori numitor nederivat - numarator nederivat or numitor derivat) supra numitor la patrat)

deci $f'(x)=\frac{(\sqrt{x^4+16})'x-\sqrt{x^4+16}(x)'}{x^2}=\frac{\frac{1}{2\sqrt{x^4+16}}(x^4+16)'x-\sqrt{x^4+16}}{x^2}=\frac{\frac{2x^4}{\sqrt{x^4+16}}-\sqrt{x^4+16}}{x^2}$
$f'(x)=\frac{\frac{2x^4}{\sqrt{x^4+16}}-\frac{x^4+16}{\sqrt{x^4+16}}}{x^2}=\frac{2x^4-x^4-16}{x^2\sqrt{x^4+16}}}=\frac{x^4-16}{x^2\sqrt{x^4+16}}}=\frac{(x^2-4)(x^2+4)}{x^2\sqrt{x^4+16}}}$