Anonymous
Anonymous asked in Education & ReferenceHomework Help · 8 years ago

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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  • 8 years ago
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    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.

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