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Home Exponential and Logartihmic Functions Derivatives and Integrals Involving ln x Theorem 1 (Logarithmic Differentiation)
 
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Theorem 1 (Logarithmic Differentiation)

Sometimes it is easier to differentiate the natural logarithm of a function y = f(x) than to differentiate the function itself. The method of computing the derivative of a function by differentiating its natural logarithm is called logarithmic differentiation.

THEOREM 1 (Logarithmic Differentiation)

Suppose the function y = f(x) is differentiable and not zero at x. Then

08_exp-log_functions-367.gif

PROOF

08_exp-log_functions-368.gif

Logarithmic differentiation is useful when the function is a product or involves an exponent, because logarithms turn exponents into products and products into sums.
Home Exponential and Logartihmic Functions Derivatives and Integrals Involving ln x Theorem 1 (Logarithmic Differentiation)

Last Update: 2006-11-16