How do you find the derivative of y=tan^2(x^4)?

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  1. just the chain rule

    y = u^2 where u = tan(v) and v = x^4
    y' = 2u u'
    y' = 2u sec^2(v) v'
    = 2u sec^2(v) (4x^3)
    = 8x^3 tan(x^4) sec^2(x^4)

    and, as usual, you can massage trig functions in various ways.

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  2. dy/dx = 2tan (x^4) * sec^2 (x^4) * 4x^3

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