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$$$e^{x} + \sin{\left(y z \right)}$$$ 對 $$$x$$$ 的導數
您的輸入
求$$$\frac{d}{dx} \left(e^{x} + \sin{\left(y z \right)}\right)$$$。
解答
和/差的導數等於導數的和/差：
$${\color{red}\left(\frac{d}{dx} \left(e^{x} + \sin{\left(y z \right)}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(e^{x}\right) + \frac{d}{dx} \left(\sin{\left(y z \right)}\right)\right)}$$常數的導數為$$$0$$$：
$${\color{red}\left(\frac{d}{dx} \left(\sin{\left(y z \right)}\right)\right)} + \frac{d}{dx} \left(e^{x}\right) = {\color{red}\left(0\right)} + \frac{d}{dx} \left(e^{x}\right)$$指數函數的導數為 $$$\frac{d}{dx} \left(e^{x}\right) = e^{x}$$$：
$${\color{red}\left(\frac{d}{dx} \left(e^{x}\right)\right)} = {\color{red}\left(e^{x}\right)}$$因此，$$$\frac{d}{dx} \left(e^{x} + \sin{\left(y z \right)}\right) = e^{x}$$$。
答案
$$$\frac{d}{dx} \left(e^{x} + \sin{\left(y z \right)}\right) = e^{x}$$$A
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