The necessary and sufficient conditions for the derivative function f(x) of 1. to be derivable at point x0 are that the left limit lim(h→-0)[f(x0+h)-f(x0)]/h and the right limit lim(h→+0)[f(x0+h)- are at point x0.

2. The function f(x) is derivable at the point x0 = >; Functions are continuous at this point; The function f(x) is continuous at point x0≦ >: it can be done at this point. In other words, the continuity of a function at a certain point is a necessary condition for the function to be derivable at that point, but it is not a sufficient condition.

3. The original function can guide the derivative of the inverse function, and the derivative of the inverse function is the reciprocal of the original function.

4. The function f(x) is differentiable at the point x0 = >; This function is derivable at this point; The necessary and sufficient condition for the function f(x) to be differentiable at point x0 is that the function is differentiable at this point.