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$$$1 - \cos{\left(x \right)}$$$的导数
您的输入
求$$$\frac{d}{dx} \left(1 - \cos{\left(x \right)}\right)$$$。
解答
和/差的导数等于导数的和/差：
$${\color{red}\left(\frac{d}{dx} \left(1 - \cos{\left(x \right)}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(1\right) - \frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)}$$余弦函数的导数是$$$\frac{d}{dx} \left(\cos{\left(x \right)}\right) = - \sin{\left(x \right)}$$$：
$$- {\color{red}\left(\frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)} + \frac{d}{dx} \left(1\right) = - {\color{red}\left(- \sin{\left(x \right)}\right)} + \frac{d}{dx} \left(1\right)$$常数的导数是$$$0$$$:
$$\sin{\left(x \right)} + {\color{red}\left(\frac{d}{dx} \left(1\right)\right)} = \sin{\left(x \right)} + {\color{red}\left(0\right)}$$因此，$$$\frac{d}{dx} \left(1 - \cos{\left(x \right)}\right) = \sin{\left(x \right)}$$$。
答案
$$$\frac{d}{dx} \left(1 - \cos{\left(x \right)}\right) = \sin{\left(x \right)}$$$A
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