t + sqrt(2)的导数

该计算器将求$$$t + \sqrt{2}$$$的导数，并显示步骤。

您的输入

求$$$\frac{d}{dt} \left(t + \sqrt{2}\right)$$$。

解答

和/差的导数等于导数的和/差：

$${\color{red}\left(\frac{d}{dt} \left(t + \sqrt{2}\right)\right)} = {\color{red}\left(\frac{d}{dt} \left(t\right) + \frac{d}{dt} \left(\sqrt{2}\right)\right)}$$

常数的导数是$$$0$$$:

$${\color{red}\left(\frac{d}{dt} \left(\sqrt{2}\right)\right)} + \frac{d}{dt} \left(t\right) = {\color{red}\left(0\right)} + \frac{d}{dt} \left(t\right)$$

应用幂法则 $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$，取 $$$n = 1$$$，也就是说，$$$\frac{d}{dt} \left(t\right) = 1$$$：

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

因此，$$$\frac{d}{dt} \left(t + \sqrt{2}\right) = 1$$$。

答案

$$$\frac{d}{dt} \left(t + \sqrt{2}\right) = 1$$$A

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