f ( x ) = <msubsup> &#x222B;<!-- ∫ --> <mrow class="MJX-TeXAtom-ORD">

$f\left(x\right)={\int }_{0}^{\mathrm{sin}x}1+\mathrm{sin}\left(\mathrm{sin}\left(t\right)\right)dt$
Find $\left({f}^{-1}{\right)}^{\prime }\left(0\right)$
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Blaze Frank

Just find f'(0) and then you are done.