Problem 690 (difficulty: 3/10)

Calculate the derivative of the following functions.

\(\displaystyle x^2e^{x^2+\cos x^2} \qquad \log_{\cth^2x+1}\ctg\frac{5^{\tg x}}{\ch x} \qquad \frac{\displaystyle\frac{2^{\ln x/2}}x+\arcth x}{\root3\of{x}+\root5\of{x}} \qquad \frac{\displaystyle \frac{\tg x}{x^2+1}\cdot \frac{\sqrt{x}\cdot 10^x}{\log_3x+x\ctg x} }{\displaystyle (x+1)(x^2+x^e)\cos x} \)

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