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Continuity And Differentiability

Question

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Differentiate the following function w.r.t.x: $straight x space sec to the power of negative 1 end exponent straight x$

Solution

Let space space space space space straight y equals straight x space sec to the power of negative 1 end exponent straight x therefore space dy over dx equals straight x. straight d over dx left parenthesis sec to the power of negative 1 end exponent straight x right parenthesis plus sec to the power of negative 1 end exponent straight x. straight d over dx left parenthesis straight x right parenthesis space space space space space space space space space space space space space equals straight x. fraction numerator 1 over denominator straight x square root of straight x squared minus 1 end root end fraction plus sec to the power of negative 1 end exponent straight x.1 equals fraction numerator 1 over denominator square root of straight x squared minus 1 end root end fraction plus sec to the power of negative 1 end exponent straight x

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