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Calculus

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Find the derivative of y with respect to x:
y=(1+cos²x)^6
y'=6(1+cos²x)^5

How do you derive inside the brackets? The answer says -sin2x, but wouldn't it be -2sinx, using the chain rule.

  • Calculus -

    You still have to differentiate the "inside"

    d(1+cos^2x) = 2cosx(-sinx)
    = -2sinxcox
    = -sin 2x, one of the identities

    so
    y'=6(1+cos²x)^5(-sin2x)
    = y'= -6(1+cos²x)^5(sin2x)

  • Calculus -

    Oh, I see it now, thanks!

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