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:

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

= ⎛

= ʹ = ʹʹ

=

( ) ( )

= ʹʹ = ʹʹʹ d dx f x f x( ) ( ), .etc

The tangent line at a point P(x, y) of the curve y = f(x) has a slope f′(x) provided that f′(x) exists at P. The slope at P is defined to be that of the tangent line at P. The tangent line at P(x1, y1) is given by

y y f x x x− = ʹ −1 1 1( )†( ).