Question

what is the derivative of Absolute x / x by definition?

Answer 1

\[{|x| \over x}\] is not continuous

Answer 2

for x>0 |x|=x
for x<0 |x|=-x
correct?

Answer 3

So for your function the right derivative and the left derivative of 0 will be different so the derivative at x=0 will not exist

Answer 4

can you show me the steps?

Answer 5

Can I show you the steps for for
x>0 |x|=x
x<0 |x|=-x
?

Answer 6

This is by definition.

Answer 7

|x|=x whenever x>0
|x|=-x whenever x<0
|x|=0 whenever x=0

|x|/x=x/x when x>0

|x|/x=-x/x when x<0

The derivative doesn't exist at x=0 because the function didn't exist at x=0

Answer 8

Now I haven't differentiated our piecewise function yet

Answer 9

I'm sure you can do (x/x)' for x>0
and (-x/x)' for x<0

since both of these functions are constants

Answer 10

if by using the differentiation principle?

Answer 11

Find the absolute maximum and minimum of function x-2sinx over a interval [-pi,pi]