Problem 661 (difficulty: 3/10)

Calculate the derivative:

\(\displaystyle \sin x^2 \qquad e^{\tg x} \qquad \log_3(\ctg^2x) \qquad \arc\tg(x^2+1) \qquad \sin\Big(\arch\big(\arc\cos(\log_5x)\big)\Big) \)

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