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Differentiate the functions with respect to x in cos x raised to 1 by 2

Differentiate the functions with respect to x in 

\cos ( \sqrt x )

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Let us assume   :                 y\ =\ \cos ( \sqrt x )

Differentiating y with respect to x, we get  :

                                          \frac{dy}{dx}\ =\ \frac{d(\cos ( \sqrt x ))}{dx}

or                                       =\ - \sin \sqrt{x}.\frac{d( \sqrt x )}{dx}

or                                       =\ \frac{- \sin \sqrt{x}}{2\sqrt{x}}                      

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