calculus product rule

Let y = log u, u = tan t, t = x/2 From the above example, it is clear that chain rule can be extended. Let v = f(u), u = g(x), x = h(t) Then, we hav..

(1) While integration by parts, the proper choice of first function and second function is significant Try integrating Taking x as the first function and e x as the second function is simpler than taking x as the second function. (2) Integrating by parts may not be applicable to product..

A first - order first - degree differential equation is of the form If the function f turns out to be of the form f(x, y) = p(x) q(y) .(2) (i.e., the product of a function of x with a function of y, then the differential equation (1) is said to have the variable x, y separable.) In thi..

Limits- operations on functions Continuity of a function Intermediate value, extreme value theorem Derivatives, differentiability Derivatives of functions Chain rule Rolle's theorem, mean value theorem, and L'Hopital's rule Maxima, minima, inflection points, intervals Newton's m..

Events are said to be independent if the occurrence of one event does not affect the occurrence of others. If A and B are two independent events, then This is known as Multiplication Rule of Probability . The converse is also true, that is if two events A and B asso..

Dot Product of Vectors and the Resolution of a Vector - It was mentioned earlier that, displacement vectors are added to displacement vectors, or velocity vectors are added to velocity vectors. Just as it is meaningless to add scalar quantities of different kinds, such as mass and tempera..

The emf of a cell is positive when one moves in the direction of increasing potential (i.e., negative pole to positive pole) through the cell and is negative when one moves from positive to negativ..

Expression for the equilibrium constant of a reaction is written in the form of a ratio. The numerator consists of the molar concentration (or partial pressure) terms of the products each raised to a power equal to its stoichiometric coefficient in the balanced chemical equation, and th..

is defined to be perpendicular to the plane containing . To understand the direction of the vector , let us refer to the figure. Imagine rotating a right handed screw whose axis is perpendicular to the plane formed by a and b so as to twist it from a to b through the angle p between them. Then the ..

Function - We consider two sets A and B. We form the Cartesian Product, we form relations. From all the relations, we can select a few which satisfy the rule that each element of the set A is related to only one element of the set B. When a relation satisfies this rule..