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$$$1 - \phi$$$の導関数
入力内容
$$$\frac{d}{d\phi} \left(1 - \phi\right)$$$ を求めよ。
解答
和/差の導関数は、導関数の和/差である:
$${\color{red}\left(\frac{d}{d\phi} \left(1 - \phi\right)\right)} = {\color{red}\left(\frac{d}{d\phi} \left(1\right) - \frac{d}{d\phi} \left(\phi\right)\right)}$$$$$n = 1$$$ を用いて冪法則 $$$\frac{d}{d\phi} \left(\phi^{n}\right) = n \phi^{n - 1}$$$ を適用すると、すなわち $$$\frac{d}{d\phi} \left(\phi\right) = 1$$$:
$$- {\color{red}\left(\frac{d}{d\phi} \left(\phi\right)\right)} + \frac{d}{d\phi} \left(1\right) = - {\color{red}\left(1\right)} + \frac{d}{d\phi} \left(1\right)$$定数の導数は$$$0$$$です:
$${\color{red}\left(\frac{d}{d\phi} \left(1\right)\right)} - 1 = {\color{red}\left(0\right)} - 1$$したがって、$$$\frac{d}{d\phi} \left(1 - \phi\right) = -1$$$。
解答
$$$\frac{d}{d\phi} \left(1 - \phi\right) = -1$$$A
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