$$$2 \sinh{\left(v \right)}$$$ 的導數
您的輸入
求$$$\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right)$$$。
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 $$$c = 2$$$ 與 $$$f{\left(v \right)} = \sinh{\left(v \right)}$$$：
$${\color{red}\left(\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right)\right)} = {\color{red}\left(2 \frac{d}{dv} \left(\sinh{\left(v \right)}\right)\right)}$$雙曲正弦的導數為 $$$\frac{d}{dv} \left(\sinh{\left(v \right)}\right) = \cosh{\left(v \right)}$$$:
$$2 {\color{red}\left(\frac{d}{dv} \left(\sinh{\left(v \right)}\right)\right)} = 2 {\color{red}\left(\cosh{\left(v \right)}\right)}$$因此，$$$\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right) = 2 \cosh{\left(v \right)}$$$。
答案
$$$\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right) = 2 \cosh{\left(v \right)}$$$A
Please try a new game Rotatly