Derivative of $$$- \frac{\pi}{6} + z$$$ with respect to $$$\pi$$$
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Find $$$\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right)\right)} = {\color{red}\left(- \frac{d}{d\pi} \left(\frac{\pi}{6}\right) + \frac{dz}{d\pi}\right)}$$The derivative of a constant is $$$0$$$:
$${\color{red}\left(\frac{dz}{d\pi}\right)} - \frac{d}{d\pi} \left(\frac{\pi}{6}\right) = {\color{red}\left(0\right)} - \frac{d}{d\pi} \left(\frac{\pi}{6}\right)$$Apply the constant multiple rule $$$\frac{d}{d\pi} \left(c f{\left(\pi \right)}\right) = c \frac{d}{d\pi} \left(f{\left(\pi \right)}\right)$$$ with $$$c = \frac{1}{6}$$$ and $$$f{\left(\pi \right)} = \pi$$$:
$$- {\color{red}\left(\frac{d}{d\pi} \left(\frac{\pi}{6}\right)\right)} = - {\color{red}\left(\frac{\frac{d}{d\pi} \left(\pi\right)}{6}\right)}$$Apply the power rule $$$\frac{d}{d\pi} \left(\pi^{n}\right) = n \pi^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{d\pi} \left(\pi\right) = 1$$$:
$$- \frac{{\color{red}\left(\frac{d}{d\pi} \left(\pi\right)\right)}}{6} = - \frac{{\color{red}\left(1\right)}}{6}$$Thus, $$$\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right) = - \frac{1}{6}$$$.
Answer
$$$\frac{d}{d\pi} \left(- \frac{\pi}{6} + z\right) = - \frac{1}{6}$$$A