Question

U=(y/z) + (z/x).. Find Z.(du/dz)

Answer 1

Hey mate :

$given \: u = ( \frac{y}{z} ) + ( \frac{z}{x} )..............(1) \\ find \: z.( \frac{du}{dz} ). \\ diff \: w. \: r. \: to \: z. \\ \frac{du}{dz} = y. \frac{d}{dz} .\frac{1}{z} + \frac{1}{x}. \frac{d}{dz.} z. \\ \frac{du}{dz} = y.( - \frac{1}{ {z}^{2} } ) + \frac{1}{x} .1. \\ \frac{du}{dz} = - (\frac{ y}{ {z}^{2} } ) + \frac{1}{x} . \\ multiply \: with \: z \: in \: both \: sides. \\ z. \frac{du}{dz} = \frac{z}{x } - \frac{y}{z} .$


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