# What is the value of #F'(x)# if #F(x) = int_0^sinxsqrt(t)dt# ?

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To find ( F'(x) ) if ( F(x) = \int_{0}^{\sin x} \sqrt{t} , dt ), we differentiate ( F(x) ) with respect to ( x ) using the Fundamental Theorem of Calculus. The derivative is ( F'(x) = \sqrt{\sin x} \cdot \frac{d}{dx}(\sin x) = \sqrt{\sin x} \cdot \cos x ).

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