关于 FunctionExpand 的疑问 | 我心永恒的小站

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问题

今天我在帮忙别人求解一个问题的时候,在他的表达式中有 Abs 这个函数,在后续的处理过程中需要对 Abs 这个函数进行求导,然后绘图,原图是一个曲线,但是绘制的图像是一个间断的直线,很显然这个结果是不对的,于是我开始一步一步检查我的代码,最后落脚点我发现出现在了 Abs 这个函数的导数上

在这里我使用了函数 N ,也没有得到数值解,然后在下面的建议栏部分 Mathematica 提示我使用 FunctionExpand ,我尝试使用这个函数,确实可以,

不知道为什么会这样,希望有人可以帮我解答一下

英文提问版

Today, while helping someone solve a problem, I encountered an issue with the Abs function in their expression. I needed to derive the Abs function and then plot it. The original image was a curve, but the plot ended up as a discontinuous straight line, which is obviously wrong. So, I started to check my code step by step and found the problem lies with the derivative of the Abs function.

$$ \text{Abs}'(0.951057) $$

Here I used the N function, but I didn't get a numerical solution. Then, in the suggestion bar below, Mathematica suggested I use FunctionExpand. I tried this function, and it indeed worked.

$$ 1 $$