Main rules and examples

Chain Rule

A method for finding the derivative of a composition of functions.
The formula is . Another form of the chain rule is .

Integration by Parts

A formula used to integrate the product of two functions.

Formula:
Example 1:	Evaluate .
	Use u = x and dv = ex/2 dx. Then we get du = dx and v = 2ex/2. This can be summarized: u = x dv = ex/2 dx du = dx v = 2ex/2 It follows that

Definite Integral

An integral which is evaluated over an interval. A definite integral is written . Definite integrals are used to find the area between the graph of a function and the x-axis. There are many other applications. Formally, a definite integral is the limit of a Riemann sum as the norm of the partition approaches zero. 

That is, .

Indefinite Integral

The family of functions that have a given function as a common derivative. The indefinite integral of f(x) is written
∫ f(x) dx.