Question 1158465
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if y = sqrt(cos(x) * sqrt (cos(x) * sqrt (cos(x)* ....to ∞))). 


find dy/dx
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<pre>
Square both sides.  You will get   

    {{{y^2}}} = cos(x)*y.


Cancel "y" in both sides. You will get

    y = cos(x).


Take the derivative

    y' = -sin(x).


It is your answer.
</pre>

Solved.