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$$$u \ln\left(a\right)$$$ 對 $$$u$$$ 的導數
您的輸入
求$$$\frac{d}{du} \left(u \ln\left(a\right)\right)$$$。
解答
套用常數倍法則 $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$，使用 $$$c = \ln\left(a\right)$$$ 與 $$$f{\left(u \right)} = u$$$：
$${\color{red}\left(\frac{d}{du} \left(u \ln\left(a\right)\right)\right)} = {\color{red}\left(\ln\left(a\right) \frac{d}{du} \left(u\right)\right)}$$套用冪次法則 $$$\frac{d}{du} \left(u^{n}\right) = n u^{n - 1}$$$，取 $$$n = 1$$$，也就是 $$$\frac{d}{du} \left(u\right) = 1$$$：
$$\ln\left(a\right) {\color{red}\left(\frac{d}{du} \left(u\right)\right)} = \ln\left(a\right) {\color{red}\left(1\right)}$$因此，$$$\frac{d}{du} \left(u \ln\left(a\right)\right) = \ln\left(a\right)$$$。
答案
$$$\frac{d}{du} \left(u \ln\left(a\right)\right) = \ln\left(a\right)$$$A
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