How to find continuous function and differentiable

If you have any doubt then you can ask.

If you think smoothness of the graph of function then we always get Differentiable function, and you know all Differentiable function will be continuous on certain domain.

take f(x) = sinx or trigonometric functions , are continuous and differentiable on R

Take f(x) =e^x, polynomial in x , they are continuous and differentiable.