Differentiation is a mathematical process that involves finding the rate of change of a function with respect to its independent variable. It is used to calculate the slope or gradient of a curve at a specific point.
The purpose of differentiation is to help us understand how a function is changing at a specific point, and to find the maximum and minimum values of a function. It is also used in physics and engineering to calculate things like acceleration and velocity.
The chain rule is a rule that allows us to find the derivative of a composite function, which is a function that is made up of two or more simpler 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.
While differentiation involves finding the rate of change of a function, summation involves finding the total sum of a series of numbers or terms. It is the opposite of differentiation, as it is used to reverse the process of finding the derivative.
The purpose of summation is to find the total sum of a series of numbers or terms. It is commonly used in mathematics, statistics, and physics to calculate things like the area under a curve, the sum of a set of data, or the total distance traveled by an object.