![]() ![]() The process of finding the derivative is called differentiation. The numerical value that we obtain for the slope is called a derivative. The slope of the graph will vary continuously, and the slope at a single point on the graph represents the rate at which y is changing at that point in relation to x. Solving such equations often provides information about how quantities change. Thus, one of the most common ways to use calculus is to set up an equation containing an unknown function y f (x) y f (x) and its derivative, known as a differential equation. Plotting the graph of a non-linear function produces a curve that enables us to visualise the relationship between the input variable ( x) and its corresponding output variable ( y). The core mathematical concept which calculus is concerned with is that of the deriva- tive of a function. Calculus is the mathematics of change, and rates of change are expressed by derivatives. Functions that describe such behaviours are said to be non-linear functions. We apply differential calculus primarily to the study of non-linear behaviours. These functions tell us how one quantity (the dependent variable or output) varies in response to changes in another quantity (the independent variable or input). Differential calculus is the study of a dependent quantitys rate of change in relation to a change in an independent quantity. Both linear and non-linear behaviours can be described using mathematical functions. It is the process of finding the instantaneous rate of change of some quantity that varies in a non-linear way. Differential calculus is one of the two major branches of calculus, the other being integral calculus.
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