Question

what is differentiable function and how we can determine whether a function is differentiable or not?​

Answer 1

In Calculus, a differentiable function of one real variable is a function whose derivative exists at each point is at domain. As a result, the graph of a differentiable function must have a tangent line at each interior line in its domain, be relatively smooth, and cannot contain any break, angle, or cusp.

What makes a function not differentiable?
We can say that f is not differentiable for any value is x where a tangent cannot ‘exist’ or the tangent exists but is vertical (vertical line has undefined slope,hence undefined derivative) Below are graphs of functions that are not differentiable at x=0 for various reasons.

Answer 2

More generally, if x0 is an interior point in the domain of a function f, then f is said to be differentiable at x0 if the derivative f ′(x0) exists. This means that the graph of f has a non-vertical tangent line at the point (x0, f(x0)).