<span>Для начало преобразуем tg^3(x) = tg(x) * ( 1-cos(2x) ) / (1 +cos(2x) )</span>
<span>Теперь берем производную.</span>
<span>( tg(x) )' = 1/cos^2(x)</span>
<span>( ( 1-cos(2x)) / (1 +cos(2x)) )' = [ ( 1-cos(2x))' * (1 +cos(2x)) -( 1-cos(2x)) * (1 +cos(2x))' ] / (1 +cos(2x))^2 (производная дроби)</span>
<span>(3tgx)' = 3 / cos^2(x)</span>
<span>(3x)' = 3</span>
<span>( 1-cos(2x))' = 2*sin2x</span>
<span>( 1+cos(2x))' = - 2*sin2x</span>
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