derivation of $\displaystyle 1+sin^22x$ and derivation of $\displaystyle \frac{1}{3}-cot^32x$ Can you show me how did you get the answer?
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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
Originally Posted by Yuroichi derivation of $\displaystyle 1+\sin^{2}2x$ Can you show me how did you get the answer? $\displaystyle \begin{gathered}\frac{d}{{dx}}\left( {1 + {{\sin }^2}2x} \right) = 2\sin 2x \cdot \frac{d}{{dx}}\left( {\sin 2x} \right) = \hfill \\= 2\sin 2x\cos 2x \cdot \frac{d}{{dx}}\left( {2x} \right) = 4\sin 2x\cos 2x = 2\sin 4x. \hfill \\\end{gathered}$
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