# The Derivative ## 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 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 ### Derivative of the Inverse Function

The inverse of the function y(x) is the function x(y), we have ## Derivative of Trigonometric Functions and their Inverses Recall the definitions of the trigonometric functions ## Derivative of the Exponential and Logarithmic functions  Recall 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 functions ## Higher 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 where are the binomial coefficients. For example, we have  [Differential Equations]
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