sech 32. csch 2 u du =-coth u 33.
34. coth 2 u du = u -coth u 35.
csch ucoth u du = -csch u 39.
COMMO SUBSTITUTIO S
Definition of The Derivative
The derivative of the function f(x) at the point
is given and denoted by
Some Basic Derivatives
In the table below, u,v, and w are functions ofthe variable x. a, b, c, and n are constants (with some restrictions whenever they apply). function and e the natural base for designate the natural logarithmic .
. Recall that
Chain Rule Thelast formula
is known as the Chain Rule formula. It may be rewritten as
Another similar formula is given by
Derivative of the Inverse Function
The inverse of the function y(x) is thefunction x(y), we have
Derivative of Trigonometric Functions and their Inverses
Recall the definitions of the trigonometric functions
Derivative of the Exponential and Logarithmic functionsRecall the definition of the logarithm function with base a > 0 (with
Derivative of the Hyperbolic functions and their Inverses
Recall the definitions of the trigonometric functionsHigher Order Derivatives
Let y = f(x). We have:
In some books, the following notation for higher derivatives is also used:
Higher Derivative Formula for the Product: Leibniz Formula
whereare the binomial coefficients. For example, we have
Table of Trigonometric Identities