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in Trigonometry by (120 points)
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Find the derivative:

r = (2 tan3 2y - 1)1/2

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1 Answer

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\(r = 2(tan^3\, 2y-1 )^{\frac12}\)

\(\frac{dr}{dy}= 2\times\frac12(tan^32y-1)^\frac{-1}2 \,\frac{d}{dy}(tan^32y-1)\)

\(= (tan^32y - 1)^\frac{-1}{2} (3\times2\,tan^22y \,sec^22y)\)

\(=6\, tan^22y\,sec^22y(tan^32y - 1)^{\frac{-1}{2}}\)

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