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$$$u^{2} + 1$$$の導関数
入力内容
$$$\frac{d}{du} \left(u^{2} + 1\right)$$$ を求めよ。
解答
和/差の導関数は、導関数の和/差である:
$${\color{red}\left(\frac{d}{du} \left(u^{2} + 1\right)\right)} = {\color{red}\left(\frac{d}{du} \left(u^{2}\right) + \frac{d}{du} \left(1\right)\right)}$$冪法則 $$$\frac{d}{du} \left(u^{n}\right) = n u^{n - 1}$$$ を $$$n = 2$$$ に対して適用する:
$${\color{red}\left(\frac{d}{du} \left(u^{2}\right)\right)} + \frac{d}{du} \left(1\right) = {\color{red}\left(2 u\right)} + \frac{d}{du} \left(1\right)$$定数の導数は$$$0$$$です:
$$2 u + {\color{red}\left(\frac{d}{du} \left(1\right)\right)} = 2 u + {\color{red}\left(0\right)}$$したがって、$$$\frac{d}{du} \left(u^{2} + 1\right) = 2 u$$$。
解答
$$$\frac{d}{du} \left(u^{2} + 1\right) = 2 u$$$A
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