[tex]{\frac{P'(z)}{P(z)} = \frac{1}{z-z_1} + \frac{1}{z-z_2} + . . . + \frac{1}{z-z_n}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

where [tex]P(z)=(z-z_1)(z-z_2)...(z-z_n)[/tex]

Any hints? I've shown it works for a few specific cases..now I have to show that it works for n=k+1. I tried adding a [tex]\frac{1}{z-z_{k+1}}[/tex] term to both sides, and trying the product rule for P'(z)..but couldn't really get anywhere.

btw, these are complex functions, althought I don't think it makes a difference here.

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# Proove logarithmic differentiation by induction

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