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