Find the derivative: \(\dfrac{d}{dx}\left(\arcsin x^2\right)\)

Find the derivative: \(\dfrac{d}{dx}\left(4x + \arcsin 2x^2\right)\)

Find the derivative: \(\dfrac{d}{dx}(\arcsec 6x)\)

Find the derivative: \(\dfrac{d}{dx}[\arcsin(\cos x)]\)

If \(g(x) = \tan^{-1} x^2,\) then \(g'(1) = \mathop{?}\)

If \(f(x) = \csc^{-1} x,\) then \(\lim_{x \to 2} \dfrac{f(x) - f(2)}{x - 2} = \mathop{?}\)