Derivative of $$$\frac{2 \sqrt{3} u}{3}$$$
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Find $$$\frac{d}{du} \left(\frac{2 \sqrt{3} u}{3}\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$ with $$$c = \frac{2 \sqrt{3}}{3}$$$ and $$$f{\left(u \right)} = u$$$:
$${\color{red}\left(\frac{d}{du} \left(\frac{2 \sqrt{3} u}{3}\right)\right)} = {\color{red}\left(\frac{2 \sqrt{3}}{3} \frac{d}{du} \left(u\right)\right)}$$Apply the power rule $$$\frac{d}{du} \left(u^{n}\right) = n u^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{du} \left(u\right) = 1$$$:
$$\frac{2 \sqrt{3} {\color{red}\left(\frac{d}{du} \left(u\right)\right)}}{3} = \frac{2 \sqrt{3} {\color{red}\left(1\right)}}{3}$$Thus, $$$\frac{d}{du} \left(\frac{2 \sqrt{3} u}{3}\right) = \frac{2 \sqrt{3}}{3}$$$.
Answer
$$$\frac{d}{du} \left(\frac{2 \sqrt{3} u}{3}\right) = \frac{2 \sqrt{3}}{3}$$$A