definition of derivative

[chaarleey]

i need to find the second derivative of f(x)= x^2|x| using the definition of derivative.

i divide it into three cases. x<0 = -x^3 , x>0 = x^3 and when x=0

i use lim h->0 ((f(x)+h)-f(x) / h)
and get
when x<0

lim h->0 ((-x^3+h)+x^3 / h
and it just cancel itself? same for the other cases
im probably doing something really wrong..

 

[Deleted member 4993]

i need to find the second derivative of x^2|x| ussig the definition of derivative.
i divide it into three cases , x<0 = -x^3 , x>0 = x^3 and when x=0

i then use the formula lim h->0 (f(x)+h)-f(x))/ h
and get
lim h->0 (-x^3+h) +x^3 / h

and it all just cancel itself?
im probably doing something really wrong.

That should be:

lim h->0 [f(x+h)-f(x)]/ h

lim h->0 [(-x+h)^3 - (-x)^3] / h