$$$2 x + 2^{\frac{2}{3}}$$$的导数

和/差的导数等于导数的和/差：

$${\color{red}\left(\frac{d}{dx} \left(2 x + 2^{\frac{2}{3}}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(2 x\right) + \frac{d}{dx} \left(2^{\frac{2}{3}}\right)\right)}$$

对 $$$c = 2$$$ 和 $$$f{\left(x \right)} = x$$$ 应用常数倍法则 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$：

$${\color{red}\left(\frac{d}{dx} \left(2 x\right)\right)} + \frac{d}{dx} \left(2^{\frac{2}{3}}\right) = {\color{red}\left(2 \frac{d}{dx} \left(x\right)\right)} + \frac{d}{dx} \left(2^{\frac{2}{3}}\right)$$

应用幂法则 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = 1$$$，也就是说，$$$\frac{d}{dx} \left(x\right) = 1$$$：

$$2 {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} + \frac{d}{dx} \left(2^{\frac{2}{3}}\right) = 2 {\color{red}\left(1\right)} + \frac{d}{dx} \left(2^{\frac{2}{3}}\right)$$

常数的导数是$$$0$$$:

$${\color{red}\left(\frac{d}{dx} \left(2^{\frac{2}{3}}\right)\right)} + 2 = {\color{red}\left(0\right)} + 2$$

因此，$$$\frac{d}{dx} \left(2 x + 2^{\frac{2}{3}}\right) = 2$$$。