求$$$\frac{d^{2}}{dx^{2}} \left(\sin{\left(x \right)}\right)$$$
相关计算器: 对数求导法计算器, 带步骤的隐函数求导计算器
您的输入
求$$$\frac{d^{2}}{dx^{2}} \left(\sin{\left(x \right)}\right)$$$。
解答
求一阶导数 $$$\frac{d}{dx} \left(\sin{\left(x \right)}\right)$$$
正弦函数的导数为 $$$\frac{d}{dx} \left(\sin{\left(x \right)}\right) = \cos{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\sin{\left(x \right)}\right)\right)} = {\color{red}\left(\cos{\left(x \right)}\right)}$$因此，$$$\frac{d}{dx} \left(\sin{\left(x \right)}\right) = \cos{\left(x \right)}$$$。
接下来，$$$\frac{d^{2}}{dx^{2}} \left(\sin{\left(x \right)}\right) = \frac{d}{dx} \left(\cos{\left(x \right)}\right)$$$
余弦函数的导数是$$$\frac{d}{dx} \left(\cos{\left(x \right)}\right) = - \sin{\left(x \right)}$$$：
$${\color{red}\left(\frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)} = {\color{red}\left(- \sin{\left(x \right)}\right)}$$因此，$$$\frac{d}{dx} \left(\cos{\left(x \right)}\right) = - \sin{\left(x \right)}$$$。
因此，$$$\frac{d^{2}}{dx^{2}} \left(\sin{\left(x \right)}\right) = - \sin{\left(x \right)}$$$。
答案
$$$\frac{d^{2}}{dx^{2}} \left(\sin{\left(x \right)}\right) = - \sin{\left(x \right)}$$$A