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Calc

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deriv.
y=x(sinx)(cosx)

  • Calc -

    y=uvw
    y'=vwu' + uvw'+uwv'

    It is just algebra, and probably some trig identities.

  • Calc -

    use the product rule.
    hard way:
    (1)[(sinx)(cosx)] + {x(cosx)](cosx) + [x(sinx)](-sinx)
    = sinx cosx + xcos^2 x - xsin^2 x
    = 1/2 sin 2x + xcos 2x

    easier way:
    y = 1/2 x sin 2x
    y' = 1/2 (sin 2x) + 1/2 x (2cos 2x)
    = 1/2 sin 2x + x cos 2x

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