A series of rules have been derived for differentiating various types of functions. 9�U�\.�,��$rzA�Jq��O=-�A�Q� C�Lg�͑�OL+��#�^�\��z�0Q�E�G��.��m&� Ʒ�ȡ��. This website includes study notes, research papers, essays, articles and other allied information submitted by visitors like YOU. Thus, derivative dY/dX is slope of a function whether it is linear or non-linear and represents a change in the dependent variable due to a small change in the independent variable. Content Guidelines 2. This is graphically shown in Figure 5.7(b). We describe below these rules of differentiation. Thus, if ∆X is infinitesimally small, ∆Y /∆X measures the slope of the function at a particular point and is called the derivative of the function with respect to X. Where ‘a’ is constant. Disclaimer Copyright, Share Your Knowledge Thus. … She also tutors a wide range of standardized tests. Or you can consider it as a study of rates of change of quantities. At the limit of ∆Y/ ∆X when ∆X approaches zero, slope of the tangent such as tt at a point on a function becomes the derivative dY/dX of the function with respect to X. It will be seen that derivative dY / dX or, in other words, slope of this quadratic function is changing at different values of X. This is graphed in Figure 5.7(a). Ramya is a consummate master of Mathematics, teaching college curricula. For example, velocity is the rate of change of distance with respect to time in a particular direction. Differential calculus deals with the rate of change of one quantity with respect to another. Using the above rule for the derivative of a power function we have, dY / dX = 1 X 1.5 X1-1 = 1 X 1.5 X 0 = 1.5 X0 = 1.5. 0 Derivative of a Sum or Difference of Two Functions: The derivative of a sum of the two functions is equal to the sum of the derivatives obtained separately of the two functions. Ramya is a consummate master of Mathematics, teaching college curricula. Her specialties comprise of: Algebra, trigonometry, Calculus, differential calculus, transforms and Basic Math. It is thus evident that derivative of a function shows the change in value of the dependent variable when change in the independent variable (∆X) becomes infinitesimally small. If f is not assumed to be everywhere differentiable, then points at which it fails to be differentiable are also designated critical points. Y is independent of X. Before publishing your Articles on this site, please read the following pages: 1. Note that derivative of a function [Y=f (X)] is also written as d (fX) / dX. Ramya has been working as a private tutor for last 3 years. Share Your PPT File, Individual Demand: Meaning, Demand and Utility and Other Details. Differential calculus is the calculus (which you can think of as a rule book for calculating things) of differentials. endstream endobj startxref Differentials are, as the name implies related to differences between things. As stated above, derivative of a function represents the change in the dependent variable due to a infinitesimally small change in the independent variable and is written as dY / dX for a function Y = f (X). Then, to obtain the derivative of Y with respect to X, that is dY / dX, we first find the derivative of the two functions, Y = f(U) and U = g(X) separately and then multiply them together. %%EOF TOS4. ��O��00y�?#�} �o@� �t� We will explain below the basic rules of finding derivatives of the various types of functions. Some other examples of power function and their derivatives are: It should be noted that any variable raised to the zero power (as in our example X0) is equal to 1. Welcome to EconomicsDiscussion.net! We have plotted the values of X and corresponding values of Y to get a U-shaped parabolic curve in Figure 5.8. Therefore, the derivative of a constant function is equal to zero. Suppose variable Vis a function of the variable U, that is, Y = f (U) and variable U is a function of variable X, that is, U = g (X). Similarly, if ∆X is reduced further, slope of the straight line between the two corresponding points will go on becoming closer and closer to the slope of the tangent tt drawn at point A to the curve. Here a is the coefficient of the X term and the variable X is raised to the power b. The constant ‘a’ implies that Y does not vary as X varies, that is. In what follows we will focus on the use of differential calculus to solve certain types of optimisation problems. Optimisation techniques are an important set of tools required for efficiently managing firm’s resources. Thus rule for the derivative of power function (Y = a Xb) is. Privacy Policy3. Ramya has been working as a private tutor for last 3 years.

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