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