The process of differentiating the same function again and again is called successive differentiation. It deals with variables such as x and y, functions f (x), and the corresponding changes in the variables x and y. The derivative of f( x) with respect to g( x) is given by the formula, Differential calculus arises from the study of the limit of a quotient. Let u = f( x) and v = g( x) be two functions of x. 11 PART II AP CALCULUS REVIEW Chapter 2 Calculus Quick Reference Guide AP CALCULUS FORMULAS These pages contain just about all the formulas you need to know. Differentiation of a function with respect to another function The variable t is called the parameter of the function.Ħ. By the degree of a differential equation, when it is a polynomial equation in derivatives, we mean the highest power (positive integral index) of the highest order derivative involved in the given differential equation. If the variables x and y are functions of another variable namely t, then the functions are called a parametric functions. But equation (11) is not a polynomial equation in y and degree of such a differential equation can not be defined. For such cases, differentiation can be carried out more conveniently if we take logarithms and simplify before differentiation.ĥ. Some times, the function whose derivative is required involves products, quotients, and powers. If you want more Calculus topics covered, let me know which ones.In this section we will discuss about different techniques to obtain the derivatives of the given functions.įor the implicit function f(x,y) = 0, differentiate each term with respect to x treating y as a function of x and then collect the terms of dy/dx together on left hand side and remaining terms on the right hand side and then find dy/dx.
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