Question

Let f(x)=|sinx| use the definition of derivative to find f'(0) or show that f'(0) does not exist.

Answer 1

compute the limit from the left and from the right

Answer 2

a hint is that you have a nice sharp corner there, so the derivative will not exist
but you can still take the left and right hand limits
do you know what i mean by that

Answer 3

you mean like sin(x)cos(x)/|sinx| ?