cos(t) + 1的导数

该计算器将求$$$\cos{\left(t \right)} + 1$$$的导数，并显示步骤。

您的输入

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

解答

和/差的导数等于导数的和/差：

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

常数的导数是$$$0$$$:

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

余弦函数的导数是$$$\frac{d}{dt} \left(\cos{\left(t \right)}\right) = - \sin{\left(t \right)}$$$：

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

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

Please try a new game Rotatly