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$$$- \csc{\left(x \right)}$$$的导数
您的输入
求$$$\frac{d}{dx} \left(- \csc{\left(x \right)}\right)$$$。
解答
对 $$$c = -1$$$ 和 $$$f{\left(x \right)} = \csc{\left(x \right)}$$$ 应用常数倍法则 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dx} \left(- \csc{\left(x \right)}\right)\right)} = {\color{red}\left(- \frac{d}{dx} \left(\csc{\left(x \right)}\right)\right)}$$余割函数的导数为$$$\frac{d}{dx} \left(\csc{\left(x \right)}\right) = - \cot{\left(x \right)} \csc{\left(x \right)}$$$：
$$- {\color{red}\left(\frac{d}{dx} \left(\csc{\left(x \right)}\right)\right)} = - {\color{red}\left(- \cot{\left(x \right)} \csc{\left(x \right)}\right)}$$因此，$$$\frac{d}{dx} \left(- \csc{\left(x \right)}\right) = \cot{\left(x \right)} \csc{\left(x \right)}$$$。
答案
$$$\frac{d}{dx} \left(- \csc{\left(x \right)}\right) = \cot{\left(x \right)} \csc{\left(x \right)}$$$A
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