The differential coefficient of $f(\sin x)$ with respect to x, where $f(x)=\log x$, is

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Let $f(x)=x^2$ and $g(x)=\sin x$ for all $x \in R$. Then the set of all $x$ satisfying $(f \circ g \circ g \circ f)(x)=(g \circ g \circ f)(x)$, wheng $(f \circ g)(x)=f(g(x))$, is

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The range of the function $f(x)=\sin ^{-1}\left[x^2+\frac{1}{2}\right]+\cos ^{-1}\left[x^2-\frac{1}{2}\right]$, where [ ] is the greatest integer function, is:

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The differential coefficient of $f(\sin x)$ with respect to x, where $f(x)=\log x$, is

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