Problem 680 (difficulty: 3/10)

Calculate the derivative of the following functions.

\(\displaystyle x^3; \qquad 2^x; \qquad \log_{1/2}x; \qquad \frac1{\sqrt{x}}; \qquad e^x+3\ln x \qquad x^23^x \)

\(\displaystyle \frac{\sin x}x \qquad x^3e^x\cos x; \qquad x^3\cdot\left(\frac12\right)^x; \qquad \frac{x^2\cdot\ln x\cdot 3^x\cdot\cos x}{\sqrt x -\frac{3\sin x}{x^3}}. \)

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