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Continuity And Differentiability

Question

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Differentiate the following w.r.t.x :log7 (log x)

Solution

Let space space space space space space straight y equals log space 7 space left parenthesis log space straight x right parenthesis equals fraction numerator log left parenthesis log space straight x right parenthesis over denominator log space 7 end fraction therefore space space dy over dx equals fraction numerator 1 over denominator log space 7 end fraction open square brackets fraction numerator 1 over denominator log space straight x end fraction. straight d over dx left parenthesis log space straight x right parenthesis close square brackets equals fraction numerator 1 over denominator log space 7 end fraction open square brackets fraction numerator 1 over denominator log space straight x end fraction.1 over straight x close square brackets equals fraction numerator 1 over denominator straight x space log space straight x space log space 7 end fraction.

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