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# Need help on a trig derivative problem..?

I need help differentiating y=u(acosu+bcotu). What's tripping me up is that I don't know if i need to do product rule for each the acosu and bcotu while doing the product rule for u and (acosu+bcotu). Can somebody please help me out?

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- SqdancefanLv 78 years agoFavorite Answer
We assume that "a" and "b" are constants. In that case, the product rule does not apply inside the parentheses.

.. y = u(a*cos(u) + b*cot(u))

.. y' = u'(a*cos(u) + b*cot(u)) + u(a*-sin(u)u' + b*-csc(u)^2*u')

.. y' = u'(a*cos(u) + b*cot(u) - u(a*sin(u) + b*csc(u)^2))

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It works the same whether or not you apply the distributive property first.

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