导数题 1

默认 $\log$ 为自然对数。用乘积法则：

$$\frac{d}{dx}[x\log x]=1\cdot\log x + x\cdot\frac1x = \log x+1.$$

因此

$$\boxed{f'(x)=\log x+1}.$$

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英文解析

By default, $\log$ denotes the natural logarithm. Using the product rule:

$$\frac{d}{dx}[x\log x]=1\cdot\log x + x\cdot\frac1x = \log x+1.$$

Therefore

$$\boxed{f'(x)=\log x+1}.$$