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Continuity And Differentiability

Question

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Differentiate the following functions w.r.t.x: $square root of 1 plus cot space straight x end root$

Solution

Let space space space space space straight y equals square root of 1 plus cot space straight x end root therefore space dy over dx equals fraction numerator 1 over denominator 2 square root of 1 plus cot space straight x end root end fraction. straight d over dx left parenthesis 1 plus cot space straight x right parenthesis equals fraction numerator 1 over denominator 2 square root of 1 plus cot space straight x end root end fraction. left parenthesis negative cosec squared straight x right parenthesis space space space space space space space space space space space space space equals negative fraction numerator cosec squared straight x over denominator 2 square root of 1 plus cot space straight x end root end fraction

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