ordinary calculus. Some of the important concepts of the ordinary calculus are reviewed in Appendix B to this Chapter, §1.B.2. 1.6.2 Vector-valued Functions of a scalar Consider a vector-valued function of a scalar, for example the time-dependent displacement of a particle u u(t). In this case, the derivative is defined in the usual way, t t t ... Dec 19, 2011 · To compute the derivative, it is not correct to simply differentiate the definition at the point and arrive at the derivative. Rather, we need to compute the derivative from first principles as a limit of a difference quotient , where the function value at the point is taken as the specified value and the function value at nearby points is ... Explicit derivation: used to find the derivative of an explicit function, where y=3x+5, meaning y is clearly defined in terms of x. For y=3x+5, dy/dx=3. Implicit derivation: used to find the derivative of an implicitly defined function, where the function is defined in terms of x and y (x and y are intermixed). The derivative of the momentum of a body equals the force applied to the body; rearranging this derivative statement leads to the famous F = ma equation associated with Newton's second law of motion. The reaction rate of a chemical reaction is a derivative.Mar 08, 2015 · Pearson.Thomas.Calculus.12th.Edition Table of Contents 1. Functions 1.1 Functions and Their Graphs 1.2 Combining Functions;...