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已知函数\(f(x)={{x}^{2}}-\frac {1} {2}x.\)
求\(f\left ( {x} \right )\)在\(x = 1\)处的导数．
参考答案：\(\frac{3}{2}\)
解析：
\(\because \Delta y=f(x+\Delta x)-f(x)\)\(={(\Delta x{)}^{2}}+2x\cdot \Delta x-\frac {1} {2}\Delta x\)
\(\therefore \frac {\Delta y} {\Delta x}=2x+\Delta x-\frac {1} {2}\)
\(\therefore {{f}^{\prime }}(x)=\mathop{\lim}\limits_{\Delta x\to 0}\frac {\Delta y} {\Delta x}=2x-\frac {1} {2}\)．
\({f^\prime }(1) = 2 \times 1 - \frac{1}{2} = \frac{3}{2}\)
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