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$$$2 \theta$$$の導関数
入力内容
$$$\frac{d}{d\theta} \left(2 \theta\right)$$$ を求めよ。
解答
定数倍の法則 $$$\frac{d}{d\theta} \left(c f{\left(\theta \right)}\right) = c \frac{d}{d\theta} \left(f{\left(\theta \right)}\right)$$$ を $$$c = 2$$$ と $$$f{\left(\theta \right)} = \theta$$$ に対して適用します:
$${\color{red}\left(\frac{d}{d\theta} \left(2 \theta\right)\right)} = {\color{red}\left(2 \frac{d}{d\theta} \left(\theta\right)\right)}$$$$$n = 1$$$ を用いて冪法則 $$$\frac{d}{d\theta} \left(\theta^{n}\right) = n \theta^{n - 1}$$$ を適用すると、すなわち $$$\frac{d}{d\theta} \left(\theta\right) = 1$$$:
$$2 {\color{red}\left(\frac{d}{d\theta} \left(\theta\right)\right)} = 2 {\color{red}\left(1\right)}$$したがって、$$$\frac{d}{d\theta} \left(2 \theta\right) = 2$$$。
解答
$$$\frac{d}{d\theta} \left(2 \theta\right) = 2$$$A
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