cos(x) + 5 的導數

此計算器將求出 $$$\cos{\left(x \right)} + 5$$$ 的導數，並顯示步驟。

您的輸入

求$$$\frac{d}{dx} \left(\cos{\left(x \right)} + 5\right)$$$。

解答

和/差的導數等於導數的和/差：

$${\color{red}\left(\frac{d}{dx} \left(\cos{\left(x \right)} + 5\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(\cos{\left(x \right)}\right) + \frac{d}{dx} \left(5\right)\right)}$$

餘弦函數的導數為 $$$\frac{d}{dx} \left(\cos{\left(x \right)}\right) = - \sin{\left(x \right)}$$$：

$${\color{red}\left(\frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)} + \frac{d}{dx} \left(5\right) = {\color{red}\left(- \sin{\left(x \right)}\right)} + \frac{d}{dx} \left(5\right)$$

常數的導數為$$$0$$$：

$$- \sin{\left(x \right)} + {\color{red}\left(\frac{d}{dx} \left(5\right)\right)} = - \sin{\left(x \right)} + {\color{red}\left(0\right)}$$

因此，$$$\frac{d}{dx} \left(\cos{\left(x \right)} + 5\right) = - \sin{\left(x \right)}$$$。

答案

$$$\frac{d}{dx} \left(\cos{\left(x \right)} + 5\right) = - \sin{\left(x \right)}$$$A