Question

Using chain rule, what is the derivative of arcsin(sin(x))

Answer 1

Chain rule:
if
y=y(u) and u=u(x)
The dy/dx=(dv/du)(du/dx)

In our case
y=arcsin(u)
u=sin(x)

dy/du=1/√(1-u²) = 1/√(1-sin²x)
du/dx=cos x

dy/dx=cos x /√(1-sin²x)

Answer: dy/dx=cos x /√(1-sin²x)