Most of the things in the universe are dynamic or always changing. If we can somehow find out the measure of the rate of change of any quantity, it is possible to predict the outcome in the future. That is how our scientists and researchers analyze the future and plan for it. If you are still wondering how to calculate the rate of change of a quantity, the answer lies in the term ‘Differentiation’.
What Is Differentiation in Maths
Differentiation is a simple but powerful mathematical technique to predict the outcome of an event at an unknown instant. Differentiation can only be used to calculate the rate of change of a function and thus the first thing you need is the representation of a quantity in the form of a function of its variable. A function is differentiated with respect to the variables and its outcome denotes the rate of change of a function with respect to that variable.
If you know what is differentiation in Maths, you can solve many real life problems related to prediction. Suppose we have a mathematical function for the amount of air pollution in terms of time as a variable. Now, the differentiation of this function with respect to time will indicate the rate of change of air pollution with time. If the time (t) in the function is in years, the result of the differentiation will represent the rate of change of pollution per unit year.
The notation f (x) represents a function f with x as variable. The differentiation of this function will be represented by d/dx f(x). A function may be complex and there are various formulas to find out differentiation of various types of functions.
Now that you know, what is Differentiation in Maths; let us try to understand the range of values of differentiation and their significance. The result of differentiation can have any real value from -∞ to +∞ including 0. A positive value for the differentiation of a function of time indicates that its value is increasing with time while a negative value indicates that it is decreasing with time. A 0 value indicates that it does not change with time.
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