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$$$\cosh{\left(u \right)} \left|{a}\right|$$$ 對 $$$u$$$ 的導數
您的輸入
求$$$\frac{d}{du} \left(\cosh{\left(u \right)} \left|{a}\right|\right)$$$。
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 $$$c = \left|{a}\right|$$$ 與 $$$f{\left(u \right)} = \cosh{\left(u \right)}$$$：
$${\color{red}\left(\frac{d}{du} \left(\cosh{\left(u \right)} \left|{a}\right|\right)\right)} = {\color{red}\left(\left|{a}\right| \frac{d}{du} \left(\cosh{\left(u \right)}\right)\right)}$$雙曲餘弦函數的導數為$$$\frac{d}{du} \left(\cosh{\left(u \right)}\right) = \sinh{\left(u \right)}$$$：
$$\left|{a}\right| {\color{red}\left(\frac{d}{du} \left(\cosh{\left(u \right)}\right)\right)} = \left|{a}\right| {\color{red}\left(\sinh{\left(u \right)}\right)}$$因此，$$$\frac{d}{du} \left(\cosh{\left(u \right)} \left|{a}\right|\right) = \sinh{\left(u \right)} \left|{a}\right|$$$。
答案
$$$\frac{d}{du} \left(\cosh{\left(u \right)} \left|{a}\right|\right) = \sinh{\left(u \right)} \left|{a}\right|$$$A
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