Editing Logarithmic derivative (section)

==Computing ordinary derivatives using logarithmic derivatives==
{{Main|Logarithmic differentiation}}
Logarithmic derivatives can simplify the computation of derivatives requiring the [[product rule]] while producing the same result.  The procedure is as follows: Suppose that {{nowrap|<math>f(x) = u(x)v(x)</math>}} and that we wish to compute <math>f'(x)</math>.  Instead of computing it directly as {{nowrap|<math>f' = u'v + v'u</math>}}, we compute its logarithmic derivative.  That is, we compute:
<math display="block">\frac{f'}{f} = \frac{u'}{u} + \frac{v'}{v}.</math>

Multiplying through by ƒ computes {{math|''f''&prime;}}:
<math display="block">f' = f\cdot\left(\frac{u'}{u} + \frac{v'}{v}\right).</math>

This technique is most useful when ƒ is a product of a large number of factors.  This technique makes it possible to compute {{math|''f''&prime;}} by computing the logarithmic derivative of each factor, summing, and multiplying by {{math|''f''}}.

For example, we can compute the logarithmic derivative of <math>e^{x^2}(x-2)^3(x-3)(x-1)^{-1}</math> to be <math>2x + \frac{3}{x-2} + \frac{1}{x-3} - \frac{1}{x-1}</math>.