The Derivative
The Derivative
The derivative of the function f(x) at the point 
is given and
denoted by
In the table below, u,v, and w are functions of the variable
x. a, b, c, and n are constants (with some restrictions
whenever they apply). 
designate the natural logarithmic
function and e the natural base for . Recall that 
.
Chain Rule
The last formula
is known as the Chain Rule formula. It may be rewritten as
Another similar formula is given by
The inverse of the function y(x) is the function x(y), we have
Recall the definitions of the trigonometric functions
Recall the definition of the logarithm function with base a > 0
(with 
):
Recall the definitions of the trigonometric functions
Let y = f(x). We have:
In some books, the following notation for higher derivatives is also used:
where 
are
the binomial coefficients. For example, we have
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