How do you differentiate $y=csc^-1(x/2)$ ?

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Answer 1 · 2016-11-30T02:54:11

$dy/dx=(-2)/(x^2sqrt(1-4/x^2)$

$y=csc^-1(x/2)$

$cscy = x/2$

$siny = 2/x$

$cosy dy/dx = -2/x^2$ (Implicit differentiation and Power rule)

$dy/dx = -2/x^2 * 1/cosy$

Since $cos^2y + sin^2y =1$

$cos^2y = 1-sin^2y = 1-(2/x)^2$

$cosy = sqrt(1-4/x^2)$

$dy/dx = (-2)/(x^2sqrt(1-4/x^2)$

How do you differentiate y=csc^-1(x/2)y=csc^-1(x/2)?