Calculus

Calculus Cheat Sheet Visit http://tutorial.math.lamar.edu for a complete set of Calculus notes. ? 2005 Paul Dawkins Derivatives Definition and Notation If ( )y f x= then the derivative is defined to be ( ) ( ) ( ) 0 lim h f x h f xf x h? + -? = . If ( )y f x= then all of the following are equivalent notations for the derivative. ( ) ( )( ) ( )df dy df x y f x Df xdx dx dx? ?= = = = = If ( )y f x= all of the following are equivalent notations for derivative evaluated at x a= . ( ) ( )x a x a x a df dyf a y Df adx dx= = = ? ?= = = = Interpretation of the Derivative If ( )y f x= then, 1. ( )m f a?= is the slope of the tangent line to ( )y f x= at x a= and the equation of the tangent line at x a= is given by ( ) ( )( )y f a f a x a?= + - .