$$$- \frac{\pi}{6} + z$$$ 关于 $$$\pi$$$ 的导数
您的输入
求$$$\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right)$$$。
解答
和/差的导数等于导数的和/差：
$${\color{red}\left(\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right)\right)} = {\color{red}\left(- \frac{d}{d\pi} \left(\frac{\pi}{6}\right) + \frac{dz}{d\pi}\right)}$$常数的导数是$$$0$$$:
$${\color{red}\left(\frac{dz}{d\pi}\right)} - \frac{d}{d\pi} \left(\frac{\pi}{6}\right) = {\color{red}\left(0\right)} - \frac{d}{d\pi} \left(\frac{\pi}{6}\right)$$对 $$$c = \frac{1}{6}$$$ 和 $$$f{\left(\pi \right)} = \pi$$$ 应用常数倍法则 $$$\frac{d}{d\pi} \left(c f{\left(\pi \right)}\right) = c \frac{d}{d\pi} \left(f{\left(\pi \right)}\right)$$$：
$$- {\color{red}\left(\frac{d}{d\pi} \left(\frac{\pi}{6}\right)\right)} = - {\color{red}\left(\frac{\frac{d}{d\pi} \left(\pi\right)}{6}\right)}$$应用幂法则 $$$\frac{d}{d\pi} \left(\pi^{n}\right) = n \pi^{n - 1}$$$，取 $$$n = 1$$$，也就是说，$$$\frac{d}{d\pi} \left(\pi\right) = 1$$$：
$$- \frac{{\color{red}\left(\frac{d}{d\pi} \left(\pi\right)\right)}}{6} = - \frac{{\color{red}\left(1\right)}}{6}$$因此，$$$\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right) = - \frac{1}{6}$$$。
答案
$$$\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right) = - \frac{1}{6}$$$A
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