difference btn differentiating l e^x l and e^lxl

The first function is always positive! So l e^x l = e^x

So the derivative will be the same...

e^lxl has 2 parts x<0 and x>=0

e^lxl = e^-x when x<0

and e^lxl = e^x when x > 0

This should be sufficient to find the difference?

If u still are unclear.. i will post in greater details..

I would suggest that you make the graph of both these functions for better understanding :)

because if x = -1

|x| = 1 .. so for x<0

|x| = - x

U can take the definition of |x| as

|x| = x when x>=0
|x| = -x when x<0