-sqrt(5)*sin(t)/5的导数

该计算器将求$$$- \frac{\sqrt{5} \sin{\left(t \right)}}{5}$$$的导数，并显示步骤。

您的输入

求$$$\frac{d}{dt} \left(- \frac{\sqrt{5} \sin{\left(t \right)}}{5}\right)$$$。

解答

对 $$$c = - \frac{\sqrt{5}}{5}$$$ 和 $$$f{\left(t \right)} = \sin{\left(t \right)}$$$ 应用常数倍法则 $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$：

$${\color{red}\left(\frac{d}{dt} \left(- \frac{\sqrt{5} \sin{\left(t \right)}}{5}\right)\right)} = {\color{red}\left(- \frac{\sqrt{5}}{5} \frac{d}{dt} \left(\sin{\left(t \right)}\right)\right)}$$

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

$$- \frac{\sqrt{5} {\color{red}\left(\frac{d}{dt} \left(\sin{\left(t \right)}\right)\right)}}{5} = - \frac{\sqrt{5} {\color{red}\left(\cos{\left(t \right)}\right)}}{5}$$

因此，$$$\frac{d}{dt} \left(- \frac{\sqrt{5} \sin{\left(t \right)}}{5}\right) = - \frac{\sqrt{5} \cos{\left(t \right)}}{5}$$$。

答案

$$$\frac{d}{dt} \left(- \frac{\sqrt{5} \sin{\left(t \right)}}{5}\right) = - \frac{\sqrt{5} \cos{\left(t \right)}}{5}$$$A

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