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Continuity And Differentiability

Question
CBSEENMA12034927

Differentiate :log space sin square root of straight x squared plus 1 end root

Solution
Let space space space space space straight y equals log space sin square root of straight x squared plus 1 end root
therefore space dy over dx equals fraction numerator 1 over denominator sin square root of straight x squared plus 1 end root end fraction. straight d over dx open square brackets sin square root of straight x squared plus 1 end root close square brackets
space space space space space space space space space space space space space equals fraction numerator 1 over denominator sin square root of straight x squared plus 1 end root end fraction. cos square root of straight x squared plus 1 end root. straight d over dx open parentheses square root of straight x squared plus 1 end root close parentheses
space space space space space space space space space space space space space equals fraction numerator 1 over denominator sin square root of straight x squared plus 1 end root end fraction. cos square root of straight x squared plus 1 end root. fraction numerator 2 straight x over denominator 2 square root of straight x squared plus 1 end root end fraction equals fraction numerator straight x over denominator square root of straight x squared plus 1 end root end fraction. cot square root of straight x squared plus 1 end root

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