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Continuity And Differentiability

Question

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$If space straight y equals square root of straight a plus square root of straight a plus straight x end root end root comma space find space dy over dx.$

Solution

Let space space straight y equals square root of straight a plus square root of straight a plus straight x end root end root therefore space dy over dx equals fraction numerator 1 over denominator 2 square root of straight a plus square root of straight a plus straight x end root end root end fraction. straight d over dx open parentheses straight a plus square root of straight a plus straight x end root close parentheses space space space space space space space space space space space space space equals fraction numerator 1 over denominator 2 square root of straight a plus square root of straight a plus straight x end root end root end fraction cross times open parentheses 0 plus fraction numerator 1 over denominator 2 square root of straight a plus straight x end root end fraction close parentheses equals fraction numerator 1 over denominator 4 square root of straight a plus square root of straight a plus straight x end root end root. square root of straight a plus straight x end root end fraction

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