How would you differentiate f(x)=|x^3|, or an absolute-value function?

Question

anonymous · Answer

You need to consider three different domains. $$x>0,x<0,x=0$$When x > 0, the function is just the regular x^3. When x < 0, the function becomes -x^3. The trouble comes when x = 0, you would need to use the definition of the derivative to verify if the derivative exists or not.

anonymous · Answer

Aww... no shortcuts, no rules?

anonymous · Answer

nope, its different for every function.  if the question had been about:$$f(x)=|x^3-5|$$then even the domains would be a little different. or if it was an even function, etc.  You really have to know about the graph itself.