$$$u^{3} + 1$$$ 的導數
您的輸入
求$$$\frac{d}{du} \left(u^{3} + 1\right)$$$。
解答
和/差的導數等於導數的和/差：
$${\color{red}\left(\frac{d}{du} \left(u^{3} + 1\right)\right)} = {\color{red}\left(\frac{d}{du} \left(u^{3}\right) + \frac{d}{du} \left(1\right)\right)}$$套用冪次法則 $$$\frac{d}{du} \left(u^{n}\right) = n u^{n - 1}$$$，取 $$$n = 3$$$：
$${\color{red}\left(\frac{d}{du} \left(u^{3}\right)\right)} + \frac{d}{du} \left(1\right) = {\color{red}\left(3 u^{2}\right)} + \frac{d}{du} \left(1\right)$$常數的導數為$$$0$$$：
$$3 u^{2} + {\color{red}\left(\frac{d}{du} \left(1\right)\right)} = 3 u^{2} + {\color{red}\left(0\right)}$$因此，$$$\frac{d}{du} \left(u^{3} + 1\right) = 3 u^{2}$$$。
答案
$$$\frac{d}{du} \left(u^{3} + 1\right) = 3 u^{2}$$$A