$$$x e^{8} - 9$$$ 的導數
您的輸入
求$$$\frac{d}{dx} \left(x e^{8} - 9\right)$$$。
解答
和/差的導數等於導數的和/差：
$${\color{red}\left(\frac{d}{dx} \left(x e^{8} - 9\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(x e^{8}\right) - \frac{d}{dx} \left(9\right)\right)}$$常數的導數為$$$0$$$：
$$- {\color{red}\left(\frac{d}{dx} \left(9\right)\right)} + \frac{d}{dx} \left(x e^{8}\right) = - {\color{red}\left(0\right)} + \frac{d}{dx} \left(x e^{8}\right)$$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 $$$c = e^{8}$$$ 與 $$$f{\left(x \right)} = x$$$：
$${\color{red}\left(\frac{d}{dx} \left(x e^{8}\right)\right)} = {\color{red}\left(e^{8} \frac{d}{dx} \left(x\right)\right)}$$套用冪次法則 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = 1$$$，也就是 $$$\frac{d}{dx} \left(x\right) = 1$$$：
$$e^{8} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = e^{8} {\color{red}\left(1\right)}$$因此，$$$\frac{d}{dx} \left(x e^{8} - 9\right) = e^{8}$$$。
答案
$$$\frac{d}{dx} \left(x e^{8} - 9\right) = e^{8}$$$A