Question

Derivada de
$y= \frac{arcsenx}{x}$

Answer 1

$y = \frac{arcsenx}{x}$

vamos usar a regra do quociente.

$\\ F(x) = \frac{G(x)}{H(x)} \\ \\ F(x)' = \frac{G(x)'*H(x) -G(x)*H(x)}{H(x)^2}$

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$\\ y = \frac{arcsenx}{x} \\ \\ y' = \frac{arcsenx'*x -arcsenx*x'}{x^2} \\ \\ y' = \frac{ \frac{1}{ \sqrt{1-x^2} }*x-arcsenx*1 }{x^2} \\ \\ y' = \frac{ \frac{x}{ \sqrt{1-x^2} } -arcsenx}{x^2} \\ \\ y' = \frac{ \frac{x - \sqrt{1-x^2} *arcsenx}{ \sqrt{1-x^2} } }{x^2} \\ \\ y' = \frac{x- \sqrt{1-x^2}*arcsenx }{x^2 \sqrt{1-x^2} }$