Question

Найти производные функций
$y = arccos \frac{1}{x} ;\\y = arcsin(sinx)$

Answer 1

$y=\arccos \dfrac{1}{x}\\\\y'=-\dfrac{1}{\sqrt{1-(1/x)^2}}\cdot \left(\dfrac{1}{x}\right)'=-\dfrac{1}{\sqrt{1-(1/x)^2}} \cdot \left(-\dfrac{1}{x^2}\right)=\dfrac{1}{x^2\sqrt{1-(1/x)^2}}$

$y=\arcsin (\sin x)\\\\y'=\dfrac{1}{\sqrt{1-\sin^2x}} \cdot (\sin x)'=\dfrac{\cos x}{\sqrt{\cos^2 x}}=\dfrac{\cos x}{|\cos x|}$