Question

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

Answer 1

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.

Answer 2

Aww... no shortcuts, no rules?

Answer 3

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.