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Sponsor Area

Continuity And Differentiability

Question

$Differentiate space log space straight x space straight w. straight r. straight t space 1 over straight x$

Solution

Let space space space space straight y equals log space straight x comma space straight u equals 1 over straight x equals straight x to the power of negative 1 end exponent therefore space space space space space dy over dx equals 1 over straight x comma space du over dx equals negative 1 over straight x squared Now space dy over du equals fraction numerator begin display style dy over dx end style over denominator begin display style du over dx end style end fraction equals fraction numerator begin display style 1 over straight x end style over denominator negative 1 over straight x squared end fraction equals negative 1 over straight x cross times straight x squared over 1 equals negative straight x.