Computing Ordinary Derivatives Using Logarithmic Derivatives
Logarithmic derivatives can simplify the computation of derivatives requiring the product rule. The procedure is as follows: Suppose that ƒ(x) = u(x)v(x) and that we wish to compute ƒ'(x). Instead of computing it directly, we compute its logarithmic derivative. That is, we compute:
Multiplying through by ƒ computes ƒ':
This technique is most useful when ƒ is a product of a large number of factors. This technique makes it possible to compute ƒ' by computing the logarithmic derivative of each factor, summing, and multiplying by ƒ.
Read more about this topic: Logarithmic Derivative
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