1 - cos(x)的导数

该计算器将求$$$1 - \cos{\left(x \right)}$$$的导数，并显示步骤。

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：

$${\color{red}\left(\frac{d}{dx} \left(1 - \cos{\left(x \right)}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(1\right) - \frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)}$$

常数的导数是$$$0$$$:

$${\color{red}\left(\frac{d}{dx} \left(1\right)\right)} - \frac{d}{dx} \left(\cos{\left(x \right)}\right) = {\color{red}\left(0\right)} - \frac{d}{dx} \left(\cos{\left(x \right)}\right)$$

余弦函数的导数是$$$\frac{d}{dx} \left(\cos{\left(x \right)}\right) = - \sin{\left(x \right)}$$$：

$$- {\color{red}\left(\frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)} = - {\color{red}\left(- \sin{\left(x \right)}\right)}$$

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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