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Math Help - What is the derivative of 1+sin^2[2x]?

  1. #1
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    What is the derivative of 1+sin^2[2x]?

    derivation of 1+sin^22x
    and derivation of \frac{1}{3}-cot^32x



    Can you show me how did you get the answer?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Think of this as f = 1 + u^2 where u = sin(2x)
    By the chain rule

    df/dx =df/du*du/dx = 2u du/dx = 2sin(2x)*cos(2x)*2




    Similar think of this as 1 - u^3 = cot(2x)

    go from here
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  3. #3
    Senior Member DeMath's Avatar
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    Quote Originally Posted by Yuroichi View Post
    derivation of 1+\sin^{2}2x

    Can you show me how did you get the answer?
    \begin{gathered}\frac{d}{{dx}}\left( {1 + {{\sin }^2}2x} \right) = 2\sin 2x \cdot \frac{d}{{dx}}\left( {\sin 2x} \right) =  \hfill \\= 2\sin 2x\cos 2x \cdot \frac{d}{{dx}}\left( {2x} \right) = 4\sin 2x\cos 2x = 2\sin 4x. \hfill \\\end{gathered}
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