$$$1 - 9 x^{2}$$$ 的導數
您的輸入
求$$$\frac{d}{dx} \left(1 - 9 x^{2}\right)$$$。
解答
和/差的導數等於導數的和/差：
$${\color{red}\left(\frac{d}{dx} \left(1 - 9 x^{2}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(1\right) - \frac{d}{dx} \left(9 x^{2}\right)\right)}$$常數的導數為$$$0$$$：
$${\color{red}\left(\frac{d}{dx} \left(1\right)\right)} - \frac{d}{dx} \left(9 x^{2}\right) = {\color{red}\left(0\right)} - \frac{d}{dx} \left(9 x^{2}\right)$$套用常數倍法則 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$，使用 $$$c = 9$$$ 與 $$$f{\left(x \right)} = x^{2}$$$：
$$- {\color{red}\left(\frac{d}{dx} \left(9 x^{2}\right)\right)} = - {\color{red}\left(9 \frac{d}{dx} \left(x^{2}\right)\right)}$$套用冪次法則 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = 2$$$：
$$- 9 {\color{red}\left(\frac{d}{dx} \left(x^{2}\right)\right)} = - 9 {\color{red}\left(2 x\right)}$$因此，$$$\frac{d}{dx} \left(1 - 9 x^{2}\right) = - 18 x$$$。
答案
$$$\frac{d}{dx} \left(1 - 9 x^{2}\right) = - 18 x$$$A