Differentiate the following expressions with respect to $x$, leaving your answers in terms of $x$
(a) $\cos ^{-1} \sqrt{x^3}$, giving your answer in non-trigonometric form,

[2]

(b) $\operatorname{cosec}\left(\ln \left(x^2+3\right)\right)$,

[2]

(c) $\left(x^2+1\right)^x$

[3]