How exactly do you figure out if a function is differentiable?

Can you explain it SIMPLY b/c my book is so confusing!How exactly do you figure out if a function is differentiable?
y = |x| is not differentiable at x = 0 for example.





You apply the definition of the derivative (that limit as h goes to zero) and if the limit exists, then it is differentiable (for the above case you would get different left and right hand limits). There are types of functions that are always differentiable, like polynomials, exponentials, rational functions where they are defined, etc.How exactly do you figure out if a function is differentiable?
If there's a variable, it can most likely be differentiated.