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( )†( ).