# What is the difference between continuous derivative and derivative?

What is the difference between continuous derivative and derivative? According to my teachers solution to the assignment,it seems there exits difference between continuous derivative and derivative. However, aunt Google does not tell me what I want.

Edit: Here is a example. $$f(x) = \begin{cases} \frac{1-cos2x}{x} & \text{otherwise} \\ k & \text{if x=0} \end{cases}$$

Does k is continuous but not continuous derivative at $0$?

Thanks:)

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 This is a little hard to answer without more context - my guess would be that by "continuous derivative" they mean the usual derivative, but are remarking that (for a particular function) this derivative is continuous. – Matt Pressland Oct 25 '12 at 13:49 @MattPressland I have posted a example:) – Joe Oct 29 '12 at 16:36

To show that a differentiable function need not have a continuous derivative, consider the function $f$ defined by
$$f(x)= \begin{cases} x^{2}\sin(1/x) & \text{if } x\neq 0\\ 0 & \text{otherwise. } \end{cases}$$