$$$\sqrt{6} \cosh{\left(u \right)}$$$ 的導數
您的輸入
求$$$\frac{d}{du} \left(\sqrt{6} \cosh{\left(u \right)}\right)$$$。
解答
套用常數倍法則 $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$，使用 $$$c = \sqrt{6}$$$ 與 $$$f{\left(u \right)} = \cosh{\left(u \right)}$$$：
$${\color{red}\left(\frac{d}{du} \left(\sqrt{6} \cosh{\left(u \right)}\right)\right)} = {\color{red}\left(\sqrt{6} \frac{d}{du} \left(\cosh{\left(u \right)}\right)\right)}$$雙曲餘弦函數的導數為$$$\frac{d}{du} \left(\cosh{\left(u \right)}\right) = \sinh{\left(u \right)}$$$：
$$\sqrt{6} {\color{red}\left(\frac{d}{du} \left(\cosh{\left(u \right)}\right)\right)} = \sqrt{6} {\color{red}\left(\sinh{\left(u \right)}\right)}$$因此，$$$\frac{d}{du} \left(\sqrt{6} \cosh{\left(u \right)}\right) = \sqrt{6} \sinh{\left(u \right)}$$$。
答案
$$$\frac{d}{du} \left(\sqrt{6} \cosh{\left(u \right)}\right) = \sqrt{6} \sinh{\left(u \right)}$$$A
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