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$$$4 \sin{\left(x \right)}$$$の導関数
入力内容
$$$\frac{d}{dx} \left(4 \sin{\left(x \right)}\right)$$$ を求めよ。
解答
定数倍の法則 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$ を $$$c = 4$$$ と $$$f{\left(x \right)} = \sin{\left(x \right)}$$$ に対して適用します:
$${\color{red}\left(\frac{d}{dx} \left(4 \sin{\left(x \right)}\right)\right)} = {\color{red}\left(4 \frac{d}{dx} \left(\sin{\left(x \right)}\right)\right)}$$正弦関数の導関数は$$$\frac{d}{dx} \left(\sin{\left(x \right)}\right) = \cos{\left(x \right)}$$$:
$$4 {\color{red}\left(\frac{d}{dx} \left(\sin{\left(x \right)}\right)\right)} = 4 {\color{red}\left(\cos{\left(x \right)}\right)}$$したがって、$$$\frac{d}{dx} \left(4 \sin{\left(x \right)}\right) = 4 \cos{\left(x \right)}$$$。
解答
$$$\frac{d}{dx} \left(4 \sin{\left(x \right)}\right) = 4 \cos{\left(x \right)}$$$A
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