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We'll have to differentiate with respect to x, using the product rule:
(u*v)' = u'*v + u*v'
Let u = cos x and v = ln x
y' = (cos x)'*(ln x) + (cos x)*(ln x)'
y' = -sin x*ln x + (cos x)/x
The first derivative of the function is y' = -sin x*ln x + (cos x)/x
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