sqrt(7)*sin(u)/7的导数

该计算器将求$$$\frac{\sqrt{7} \sin{\left(u \right)}}{7}$$$的导数，并显示步骤。

您的输入

求$$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right)$$$。

解答

对 $$$c = \frac{\sqrt{7}}{7}$$$ 和 $$$f{\left(u \right)} = \sin{\left(u \right)}$$$ 应用常数倍法则 $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$：

$${\color{red}\left(\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right)\right)} = {\color{red}\left(\frac{\sqrt{7}}{7} \frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}$$

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

$$\frac{\sqrt{7} {\color{red}\left(\frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}}{7} = \frac{\sqrt{7} {\color{red}\left(\cos{\left(u \right)}\right)}}{7}$$

因此，$$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right) = \frac{\sqrt{7} \cos{\left(u \right)}}{7}$$$。

答案

$$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right) = \frac{\sqrt{7} \cos{\left(u \right)}}{7}$$$A