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$$$1 - \cos{\left(x \right)}$$$の導関数
入力内容
$$$\frac{d}{dx} \left(1 - \cos{\left(x \right)}\right)$$$ を求めよ。
解答
和/差の導関数は、導関数の和/差である:
$${\color{red}\left(\frac{d}{dx} \left(1 - \cos{\left(x \right)}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(1\right) - \frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)}$$余弦関数の導関数は$$$\frac{d}{dx} \left(\cos{\left(x \right)}\right) = - \sin{\left(x \right)}$$$:
$$- {\color{red}\left(\frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)} + \frac{d}{dx} \left(1\right) = - {\color{red}\left(- \sin{\left(x \right)}\right)} + \frac{d}{dx} \left(1\right)$$定数の導数は$$$0$$$です:
$$\sin{\left(x \right)} + {\color{red}\left(\frac{d}{dx} \left(1\right)\right)} = \sin{\left(x \right)} + {\color{red}\left(0\right)}$$したがって、$$$\frac{d}{dx} \left(1 - \cos{\left(x \right)}\right) = \sin{\left(x \right)}$$$。
解答
$$$\frac{d}{dx} \left(1 - \cos{\left(x \right)}\right) = \sin{\left(x \right)}$$$A
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