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