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Find the derivative. Simplify where possible.

$ g(t) = t \coth \sqrt {t^2 + 1} $

$g^{\prime}(t)=c$ oth $\sqrt{t^{2}+1}-\frac{t^{2}}{\sqrt{t^{2}+1}}\left(\operatorname{csch}^{2} \sqrt{t^{2}+1}\right)$

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