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Derivative of $$$\sqrt{2} \sqrt{t}$$$
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Your Input
Find $$$\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$ with $$$c = \sqrt{2}$$$ and $$$f{\left(t \right)} = \sqrt{t}$$$:
$${\color{red}\left(\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right)\right)} = {\color{red}\left(\sqrt{2} \frac{d}{dt} \left(\sqrt{t}\right)\right)}$$Apply the power rule $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$ with $$$n = \frac{1}{2}$$$:
$$\sqrt{2} {\color{red}\left(\frac{d}{dt} \left(\sqrt{t}\right)\right)} = \sqrt{2} {\color{red}\left(\frac{1}{2 \sqrt{t}}\right)}$$Thus, $$$\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right) = \frac{\sqrt{2}}{2 \sqrt{t}}$$$.
Answer
$$$\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right) = \frac{\sqrt{2}}{2 \sqrt{t}}$$$A