Differentiation is a mathematical process used to find the rate of change of a function at a specific point. It involves calculating the slope of the curve at that point, also known as the derivative.
Differentiation and continuity are closely related concepts in calculus. A function is said to be continuous if it has no breaks or jumps in its graph. When a function is differentiable, it is also continuous. This means that if a function is differentiable at a point, it is also continuous at that point.
A differentiability point is a point on a function where the derivative exists. In other words, the slope of the function can be calculated at that point. For a function to be differentiable at a point, it must also be continuous at that point.
The main difference between differentiability and continuity is that differentiability focuses on the rate of change of a function, while continuity focuses on the smoothness of a function. A function can be continuous but not differentiable, but it cannot be differentiable without also being continuous.
The chain rule is a rule in calculus used to find the derivative of a composition of functions. It states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function. In other words, it allows us to find the rate of change of a function within a function.