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Computing Derivatives

Terms

Introduction and Summary

Derivatives of Elementary Functions

Natural Logarithm  -  There is a unique positive number e such that the function f (t) = e t is its own derivative. The natural logarithm of a positive real number x is the logarithm of x with base e , denoted log(x) . Alternately,

log(x) =    

Chain Rule  -  The formula for the derivative of a composition of functions. If h(x) = f o g(x) = f (g(x) , then:

h'(x) = f'(g(x))g'(x).    

Implicit Differentiation  -  A method for differentiating implicit functions, without necessarily solving for them, by differentiating the terms of the defining equation.
Product Rule  -  The formula for the derivative of a product of functions:

[f (x)g(x)] = f (x)g'(x) + g(x)f'(x)    

Quotient Rule  -  The formula for the derivative of a quotient of functions (which is a consequence of the product rule). If q(x) = f (x)/g(x) , then:

q'(x) =    

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