# How to differentiate e^|x|

1. Sep 5, 2008

### takercena

1. The problem statement, all variables and given/known data
a)How to differentiate fx=e^|x|?
b)Why when x = 0, f'(x) is undefined

2. Relevant equations

3. The attempt at a solution
Is it d/dx e^|x| = e^|x|? I have no idea for this question.

Last edited: Sep 5, 2008
2. Sep 5, 2008

### Dick

Re: Differentiation

|x|=x if x>=0 and |x|=(-x) if x<0. Split the problem into those two cases. To find out what happens AT x=0 look at the limits from both sides.

3. Sep 5, 2008

### takercena

Re: Differentiation

So there are two answer right? -1/e^x and e^x. Why f'x is undefined at x = 0?

4. Sep 5, 2008

### takercena

Re: Differentiation

Hello, please i still don't get it. I sketch 2 graph from the equation and at x = 0, there is a line there. But why f'(x) for e^|x| is undefined when x = 0?

5. Sep 5, 2008

### tiny-tim

Hi takercena!

Your sketch shows two graphs, reflections of each other, joined together …

do they join smoothly, or with a corner?

6. Sep 5, 2008

### Dick

Re: Differentiation

There aren't really two answers, it just that the formula for the answer looks different for x>0 than it does for x<0. If x is close to 0 and negative f'(x)~(-1), if positive then f'(x)~1. There's a sharp corner on the graph of f(x) at x=0, just like on |x|. So f(x) doesn't have a well defined slope there.

7. Sep 5, 2008

### takercena

Re: Differentiation

Oh i see. Thanks