/sci/ - Science & Math

fucking latex.. take 2:
why is the derivative of [math]f(x)=3-\frac{12}{x^{2}}[/math] positive [math]{f(x)}'=\frac{24}{x^{3}}[/math] and not negative [math]{f(x)}'=-\frac{24}{x^{3}}[/math]?
and what does the [ ] of [math]{\frac{f(x)}{g(x)}}'=\frac{{f(x)}'*g(x)-{g(x)}'*f(x)}{[g(x)]^{2}}[/math] mean? does it have to do with this?

why is the derivative of [math]f(x)=3-\frac{12}{x^{2}}[/math] [math]{f(x)}'=\frac{24}{x^{3}}[/math] and not [math]{f(x)}'=-\frac{24}{x^{3}}[/math]?
and what does the [ ] of [math][g(x)]^{2}[/math] in [math]{\frac{f(x)}{g(x)}}'=\frac{{f(x)}'*g(x)-{g(x)}'*f(x)}{[g(x)]^{2}}[/math] mean? does it have to do with this?