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$$$\frac{\sqrt{3} \sinh{\left(v \right)}}{2}$$$ 的導數
您的輸入
求$$$\frac{d}{dv} \left(\frac{\sqrt{3} \sinh{\left(v \right)}}{2}\right)$$$。
解答
套用常數倍法則 $$$\frac{d}{dv} \left(c f{\left(v \right)}\right) = c \frac{d}{dv} \left(f{\left(v \right)}\right)$$$，使用 $$$c = \frac{\sqrt{3}}{2}$$$ 與 $$$f{\left(v \right)} = \sinh{\left(v \right)}$$$：
$${\color{red}\left(\frac{d}{dv} \left(\frac{\sqrt{3} \sinh{\left(v \right)}}{2}\right)\right)} = {\color{red}\left(\frac{\sqrt{3}}{2} \frac{d}{dv} \left(\sinh{\left(v \right)}\right)\right)}$$雙曲正弦的導數為 $$$\frac{d}{dv} \left(\sinh{\left(v \right)}\right) = \cosh{\left(v \right)}$$$:
$$\frac{\sqrt{3} {\color{red}\left(\frac{d}{dv} \left(\sinh{\left(v \right)}\right)\right)}}{2} = \frac{\sqrt{3} {\color{red}\left(\cosh{\left(v \right)}\right)}}{2}$$因此，$$$\frac{d}{dv} \left(\frac{\sqrt{3} \sinh{\left(v \right)}}{2}\right) = \frac{\sqrt{3} \cosh{\left(v \right)}}{2}$$$。
答案
$$$\frac{d}{dv} \left(\frac{\sqrt{3} \sinh{\left(v \right)}}{2}\right) = \frac{\sqrt{3} \cosh{\left(v \right)}}{2}$$$A
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