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Continuity And Differentiability

Question

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Differentiate the following w.r.t.x : $sec left parenthesis tan left parenthesis square root of straight x right parenthesis right parenthesis$

Solution

Let space space space space space straight y equals sec left parenthesis tan left parenthesis square root of straight x right parenthesis right parenthesis therefore space dy over dx equals straight d over dx left square bracket sec left parenthesis tan left parenthesis square root of straight x right parenthesis right parenthesis right square bracket space space space space space space space space space space space space space equals sec left parenthesis tan left parenthesis square root of straight x right parenthesis right parenthesis tan left parenthesis tan square root of straight x right parenthesis. straight d over dx left parenthesis tan square root of straight x right parenthesis space space space space space space space space space space space space space equals sec left parenthesis tan left parenthesis square root of straight x right parenthesis right parenthesis tan left parenthesis tan square root of straight x right parenthesis. sec squared square root of straight x. straight d over dx left parenthesis square root of straight x right parenthesis space space space space space space space space space space space space space equals sec left parenthesis tan left parenthesis square root of straight x right parenthesis right parenthesis tan left parenthesis tan square root of straight x right parenthesis. sec squared square root of straight x. fraction numerator 1 over denominator 2 square root of straight x end fraction therefore space dy over dx equals fraction numerator 1 over denominator 2 square root of straight x end fraction sec squared square root of straight x sec left parenthesis tan square root of straight x right parenthesis tan left parenthesis tan square root of straight x right parenthesis

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