# Tagged Questions

178 views

23 views

### Filling in the derivative of the absolute value at zero

I have a function $f(x)$ such that $f(x_0)=0$ and I'm interested in the derivative $\frac{d |f(x)|}{dx}$ evaluated at the point $x_0$. I realize that this is usually undefined. However, if ...
94 views

### Why is $f(x)=|x|$ not differentiable?

Consider the function $f(x)=|x|$, I know that $f$ is not differentiable at $x=0$, but still, when you try to differentiate $f(x)=\sqrt{x^2}$ (which is exactly the same), you get: ...
37 views

### How to take derivative of sums of absolute values

Take the derivative of $f(m) = \sum_i | x_i - m |$. I've been told that derivative of each term is +1 or -1. How do you show that?
24 views

### Calculate the area that the following graphs form

I have been trying and trying to solve the following problem (I even used wolframalpha as an extra help, but no success, and I have like 100 calculations in my notebook): The Task: Calculate the ...
126 views

5k views

### Derivatives of functions involving absolute value

I noticed that if the absolute value definition $\lvert{x}\rvert=\sqrt{x^2}$ is used then we can get derivatives of functions with absolute value, without having to redefine them as piece-wise. For ...
281 views

### The relationship between the derivative of $f(x)$ and $|f(x)|$

I have seen it in an exercise book. I don't know how to do it. If $f(x)$ is continuous at $x=a,$ and $|f(x)|$ can be differentiated at $x=a,$ then $f(x)$ is differentiable at $x=a.$
If $f:U\subset\mathbb{C}\mapsto\mathbb{C}$, where $f(x+iy)=u(x,y)+iv(x,y)$ is a meromorphic function and if $f$, $f'$, and $f''$ are not zero in the strip $a<x<b$, can we get ...