Calculus

How do you find the derivative of f(x)=sin2x/cos2x

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  1. easy way:
    sin2x/cos2x = tan2x
    so the derivative is just

    2sec^2(2x)

    hard way, using the quotient rule:

    [2cos(2x)cos(2x) - sin(2x)(-2sin(2x))]/cos^2(2x)

    2(cos^2(2x)+sin^2(2x))/cos^2(2x)

    2/cos^2(2x)

    2sec^2(2x)

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