Question

Calcule a derivada da funcao dada abaixo
$\frac{(\sqrt{x}+a)}{(\sqrt{x}-a)}$

Answer 1

$f(x)=\dfrac{\sqrt{x}+a}{\sqrt{x}-a}\\ \\ f(x)=1+\dfrac{2a}{\sqrt{x}-a}\\ \\ f'(x)=-\dfrac{2a(\sqrt{x}-a)'}{(\sqrt{x}-a)^2}\\ \\ f'(x)=-\dfrac{2a\left(\frac{1}{2\sqrt{x}}\right)}{(\sqrt{x}-a)^2}\\ \\ f'(x)=-\dfrac{\dfrac{a}{\sqrt{x}}}{(\sqrt{x}-a)^2}\\ \\ f'(x)=-\dfrac{a}{\sqrt{x}(x-2a\sqrt{x}+a^2)}\\ \\ \boxed{f'(x)=-\dfrac{a}{x\sqrt{x}-2a|x|+a^2\sqrt{x}}}$