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