$$$\sqrt{x} \ln\left(2\right)$$$ 的導數
您的輸入
求$$$\frac{d}{dx} \left(\sqrt{x} \ln\left(2\right)\right)$$$。
解答
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 $$$c = \ln\left(2\right)$$$ 與 $$$f{\left(x \right)} = \sqrt{x}$$$：
$${\color{red}\left(\frac{d}{dx} \left(\sqrt{x} \ln\left(2\right)\right)\right)} = {\color{red}\left(\ln\left(2\right) \frac{d}{dx} \left(\sqrt{x}\right)\right)}$$套用冪次法則 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = \frac{1}{2}$$$：
$$\ln\left(2\right) {\color{red}\left(\frac{d}{dx} \left(\sqrt{x}\right)\right)} = \ln\left(2\right) {\color{red}\left(\frac{1}{2 \sqrt{x}}\right)}$$因此，$$$\frac{d}{dx} \left(\sqrt{x} \ln\left(2\right)\right) = \frac{\ln\left(2\right)}{2 \sqrt{x}}$$$。
答案
$$$\frac{d}{dx} \left(\sqrt{x} \ln\left(2\right)\right) = \frac{\ln\left(2\right)}{2 \sqrt{x}}$$$A