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Continuity And Differentiability

Question

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Differentiate the following function w.r.t.x: $cot to the power of negative 1 end exponent square root of straight x$

Solution

Let space space space space space straight y equals cot to the power of negative 1 end exponent square root of straight x therefore space dy over dx equals negative fraction numerator 1 over denominator 1 plus open parentheses square root of straight x close parentheses squared end fraction. straight d over dx left parenthesis square root of straight x right parenthesis equals negative fraction numerator 1 over denominator 1 plus straight x end fraction. fraction numerator 1 over denominator 2 square root of straight x end fraction equals negative fraction numerator 1 over denominator 2 square root of straight x left parenthesis 1 plus straight x right parenthesis end fraction

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