A differentiable function is a type of mathematical function that has a derivative at every point in its domain. This means that the function is smooth and continuous, without any sharp corners or breaks. The derivative represents the rate of change of the function, indicating how the output value changes as the input value changes. For a function to be differentiable, it must be continuous; however, continuity alone does not guarantee differentiability. Common examples of differentiable functions include polynomial functions, exponential functions, and trigonometric functions. In contrast, functions with sharp turns, like the absolute value function, may be continuous but are not differentiable at those points.