What is the derivative of this function $y = arcsin(x/2)$ ?

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Answer 1 · 2017-12-04T12:38:13

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

Using the known result:

$d/dx arcsin(x) = 1/sqrt(1-x^2)$

In conjunction with the chain rule, we have:

$d/dx arcsin(x/2) = 1/sqrt(1-(x/2)^2) * d/dx (x/2)$
$" " = 1/sqrt(1-x^2/4) * 1/2$
$" " = 1/(2sqrt(1-x^2/4))$

What is the derivative of this function y = arcsin(x/2)y = arcsin(x/2)?