ABSTRACT

For the following equations, the symbols f(x), g(x), etc., represent functions of x. The value of a function f(x) at x = a is denoted f(a). For the function y = f(x) the derivative of y with respect to x is denoted by one of the following:

dy

dx f x D y y

x , , , .′ ′( )

Higher derivatives are as follows:

d y

dx

d

dx

dy

dx

d

dx f x f x

d y

dx

=     = ′ = ′′

=

( ) ( )

d

dx

d y

dx

d

dx f x f x

 

  = ′′ = ′′′( ) ( ), etc.