A differentiable function is a mathematical function that is continuous and has a well-defined derivative at every point in its domain. This means that the function has a smooth and continuous graph with no sharp corners or breaks, and the rate of change of the function at any point can be calculated.
A differentiable function is continuous and has a well-defined derivative at every point in its domain, while a non-differentiable function may have sharp corners, breaks, or other discontinuities in its graph. This means that a differentiable function has a smoother and more predictable behavior than a non-differentiable function.
Differentiable functions are important in mathematics because they allow us to model and analyze real-world phenomena with precise and accurate mathematical tools. They also have many applications in physics, engineering, economics, and other fields.
A function is differentiable if it is continuous and has a well-defined derivative at every point in its domain. The derivative of a function can be calculated using the limit definition or through various differentiation rules, such as the power rule, product rule, and chain rule.
No, not all functions can be differentiated. For a function to be differentiable, it must be continuous and have a well-defined derivative at every point in its domain. Functions that have sharp corners, breaks, or other discontinuities in their graphs are not differentiable. Additionally, some functions may not have a well-defined derivative at certain points, such as at points where the function is not continuous.