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$$$9 x^{2}$$$の導関数
入力内容
$$$\frac{d}{dx} \left(9 x^{2}\right)$$$ 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 $$$c = 9$$$ と $$$f{\left(x \right)} = x^{2}$$$ に対して適用します:
$${\color{red}\left(\frac{d}{dx} \left(9 x^{2}\right)\right)} = {\color{red}\left(9 \frac{d}{dx} \left(x^{2}\right)\right)}$$冪法則 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ を $$$n = 2$$$ に対して適用する:
$$9 {\color{red}\left(\frac{d}{dx} \left(x^{2}\right)\right)} = 9 {\color{red}\left(2 x\right)}$$したがって、$$$\frac{d}{dx} \left(9 x^{2}\right) = 18 x$$$。
解答
$$$\frac{d}{dx} \left(9 x^{2}\right) = 18 x$$$A
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