Question

Derivada de
$y= \frac{lnx}{x^2}$

Answer 1

$\\ y = \frac{lnx}{x^2} \\ \\ y' = \frac{Lnx'*x^2-Lnx*x^2'}{(x^2)^2} \\ \\ y' = \frac{ \frac{1}{x} *x^2-Lnx*2x}{x^4} \\ \\ y' = \frac{x-2xLnx}{x^4} \\ \\ y' = \frac{x(1-2Lnx)}{x^4} \\ \\ y' = \frac{1-2Lnx}{x^3}$

Answer 2

$\sf \displaystyle y=\frac{in\:x}{x^2}\\\\\\\frac{d}{dx}\left(\frac{inx}{x^2}\right)\\\\\\{Retire\:a\:constante}\iff:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\\\=in\frac{d}{dx}\left(\frac{x}{x^2}\right)\\\\\\=in\frac{\frac{d}{dx}\left(x\right)x^2-\frac{d}{dx}\left(x^2\right)x}{\left(x^2\right)^2}\\\\\\=in\frac{1\cdot \:x^2-2xx}{\left(x^2\right)^2}\\\\\\\to \boxed{\sf =-\frac{in}{x^2}}$