cos(t) + 1 的導數

此計算器將求出 $$$\cos{\left(t \right)} + 1$$$ 的導數，並顯示步驟。

您的輸入

求$$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right)$$$。

解答

和/差的導數等於導數的和/差：

$${\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right)\right)} = {\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right) + \frac{d}{dt} \left(1\right)\right)}$$

常數的導數為$$$0$$$：

$${\color{red}\left(\frac{d}{dt} \left(1\right)\right)} + \frac{d}{dt} \left(\cos{\left(t \right)}\right) = {\color{red}\left(0\right)} + \frac{d}{dt} \left(\cos{\left(t \right)}\right)$$

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

$${\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right)\right)} = {\color{red}\left(- \sin{\left(t \right)}\right)}$$

因此，$$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right) = - \sin{\left(t \right)}$$$。

答案

$$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right) = - \sin{\left(t \right)}$$$A

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